First, try to find the domain of the function:

Did you manage? Let's compare the answers:

Is everything right? Well done!

Now let's try to find the range of values ​​of the function:

Found? Let's compare:

Got it? Well done!

Let's work with graphs again, only now it's a little more complicated - find both the domain of definition of the function and the range of values ​​of the function.

How to find both the domain and range of a function (advanced)

Here's what happened:

I think you've figured out the graphs. Now let’s try to find the domain of definition of a function in accordance with the formulas (if you don’t know how to do this, read the section about):

Did you manage? Let's check answers:

1. , since the radical expression must be greater than or equal to zero.
2. , since you cannot divide by zero and the radical expression cannot be negative.
3. , since, respectively, for all.
4. , since you cannot divide by zero.

However, we still have one more unanswered point...

I will repeat the definition once again and emphasize it:

Did you notice? The word "single" is a very, very important element of our definition. I'll try to explain it to you with my fingers.

Let's say we have a function defined by a straight line. . At, we substitute this value into our “rule” and get that. One value corresponds to one value. We can even make a table of the different values ​​and graph this function to see for ourselves.

"Look! - you say, ““ occurs twice!” So maybe a parabola is not a function? No, it is!

The fact that “ ” appears twice is not a reason to accuse the parabola of ambiguity!

The fact is that, when calculating for, we received one game. And when calculating with, we received one game. So that's right, a parabola is a function. Look at the graph:

Got it? If not, here is a life example that is very far from mathematics!

Let's say we have a group of applicants who met while submitting documents, each of whom told in a conversation where he lives:

Agree, it is quite possible for several guys to live in one city, but it is impossible for one person to live in several cities at the same time. This is like a logical representation of our “parabola” - Several different X's correspond to the same game.

Now let's come up with an example where the dependency is not a function. Let’s say these same guys told us what specialties they applied for:

Here we have a completely different situation: one person can easily submit documents for one or several directions. That is one element sets are put into correspondence several elements multitudes. Respectively, this is not a function.

Let's test your knowledge in practice.

Determine from the pictures what is a function and what is not:

Got it? And here it is answers:

• The function is - B, E.
• The function is not - A, B, D, D.

You ask why? Yes, here's why:

In all pictures except IN) And E) There are several for one!

I am sure that now you can easily distinguish a function from a non-function, say what an argument is and what a dependent variable is, and also determine the range of permissible values ​​of an argument and the range of definition of a function. Let's move on to the next section - how to set a function?

Methods for specifying a function

What do you think the words mean? "set function"? That's right, this means explaining to everyone what function is in in this case there is a speech. Moreover, explain it in such a way that everyone understands you correctly and the function graphs drawn by people based on your explanation are the same.

How can I do that? How to set a function? The simplest method, which has already been used more than once in this article, is using the formula. We write a formula, and by substituting a value into it, we calculate the value. And as you remember, a formula is a law, a rule by which it becomes clear to us and to another person how an X turns into a Y.

Usually, this is exactly what they do - in tasks we see ready-made functions specified by formulas, however, there are other ways to set a function that everyone forgets about, and therefore the question “how else can you set a function?” baffles. Let's understand everything in order, and let's start with the analytical method.

Analytical method of specifying a function

The analytical method is to specify a function using a formula. This is the most universal, comprehensive and unambiguous method. If you have a formula, then you know absolutely everything about a function - you can make a table of values ​​​​from it, you can build a graph, determine where the function increases and where it decreases, in general, study it in full.

Let's consider the function. What's the difference?

"What does it mean?" - you ask. I'll explain now.

Let me remind you that in the notation the expression in brackets is called an argument. And this argument can be any expression, not necessarily simple. Accordingly, whatever the argument (the expression in brackets) is, we will write it instead in the expression.

In our example it will look like this:

Let's consider another task related to the analytical method of specifying a function, which you will have on the exam.

Find the value of the expression at.

I'm sure that at first you were scared when you saw such an expression, but there is absolutely nothing scary about it!

Everything is the same as in the previous example: whatever the argument (the expression in brackets) is, we will write it instead in the expression. For example, for a function.

What needs to be done in our example? Instead you need to write, and instead -:

shorten the resulting expression:

That's all!

Independent work

Now try to find the meaning of the following expressions yourself:

1. , If
2. , If

Did you manage? Let's compare our answers: We are used to the fact that the function has the form

Even in our examples, we define the function in exactly this way, but analytically it is possible to specify the function in an implicit form, for example.

Try building this function yourself.

Did you manage?

This is how I built it.

What equation did we finally derive?

Right! Linear, which means that the graph will be a straight line. Let's make a table to determine which points belong to our line:

This is exactly what we were talking about... One corresponds to several.

Let's try to draw what happened:

Is what we got a function?

That's right, no! Why? Try to answer this question with the help of a drawing. What did you get?

“Because one value corresponds to several values!”

What conclusion can we draw from this?

That's right, a function cannot always be expressed explicitly, and what is “disguised” as a function is not always a function!

Tabular method of specifying a function

As the name suggests, this method is a simple sign. Yes Yes. Like the one you and I have already made. For example:

Here you immediately noticed a pattern - the Y is three times larger than the X. And now the task to “think very carefully”: do you think that a function given in the form of a table is equivalent to a function?

Let's not talk for a long time, but let's draw!

So. We draw the function specified by the wallpaper in the following ways:

Do you see the difference? It's not all about the marked points! Take a closer look:

Have you seen it now? When we define a function in a tabular way, we display on the graph only those points that we have in the table and the line (as in our case) passes only through them. When we define a function analytically, we can take any points, and our function is not limited to them. This is the peculiarity. Remember!

Graphical method of constructing a function

The graphical method of constructing a function is no less convenient. We draw our function, and another interested person can find what the y is equal to at a certain x and so on. Graphical and analytical methods are among the most common.

However, here you need to remember what we talked about at the very beginning - not every “squiggle” drawn in the coordinate system is a function! Do you remember? Just in case, I’ll copy here the definition of what a function is:

As a rule, people usually name exactly the three ways of specifying a function that we have discussed - analytical (using a formula), tabular and graphical, completely forgetting that a function can be described verbally. Like this? Yes, very simple!

Verbal description of the function

How to describe a function verbally? Let's take our recent example - . This function can be described as “every real value of x corresponds to its triple value.” That's all. Nothing complicated. You, of course, will object - “there are so complex functions, which are simply impossible to ask verbally!” Yes, there are such, but there are functions that are easier to describe verbally than to define with a formula. For example: “each natural value of x corresponds to the difference between the digits of which it consists, while the minuend is taken to be the largest digit contained in the notation of the number.” Now let's look at how our verbal description of the function is implemented in practice:

The highest figure in given number- , respectively, is a minuend, then:

Main types of functions

Now let's move on to the most interesting part - let's look at the main types of functions with which you have worked/are working and will work in the course of school and college mathematics, that is, let's get to know them, so to speak, and give them brief description. Read more about each function in the corresponding section.

Linear function

A function of the form where, are real numbers.

The graph of this function is a straight line, so constructing a linear function comes down to finding the coordinates of two points.

The position of the straight line on the coordinate plane depends on the angular coefficient.

The scope of a function (aka the scope of valid argument values) is .

Range of values ​​- .

Quadratic function

Function of the form, where

The graph of the function is a parabola; when the branches of the parabola are directed downwards, when the branches are directed upwards.

Many properties of a quadratic function depend on the value of the discriminant. The discriminant is calculated using the formula

The position of the parabola on the coordinate plane relative to the value and coefficient is shown in the figure:

Domain

The range of values ​​depends on the extremum of the given function (vertex point of the parabola) and the coefficient (direction of the branches of the parabola)

Inverse proportionality

The function given by the formula, where

The number is called the coefficient of inverse proportionality. Depending on the value, the branches of the hyperbola are in different squares:

Domain - .

Range of values ​​- .

SUMMARY AND BASIC FORMULAS

1. A function is a rule according to which each element of a set is associated with a single element of the set.

• - this is a formula denoting a function, that is, the dependence of one variable on another;
• - variable value, or argument;
• - dependent quantity - changes when the argument changes, that is, according to any specific formula reflecting the dependence of one quantity on another.

2. Valid argument values, or the domain of a function, is what is associated with the possibilities in which the function makes sense.

3. Function range- this is what values ​​it takes, given acceptable values.

4. There are 4 ways to set a function:

• analytical (using formulas);
• tabular;
• graphic
• verbal description.

5. Main types of functions:

• : , where, are real numbers;
• : , Where;
• : , Where.

Cryptocurrency exchanges work exactly the same as regular exchanges valuable papers. An experienced trader will spend a little time looking at the price chart of BTC, ETH or another asset, but a beginner will risk a lot of money. In order to understand and learn to decipher data from the price chart, you need to understand the essence of the main “Japanese candlestick” chart, which can be found on any of the existing crypto exchanges.

Stock charts are the most important tool for market analysis, as they present information about prices in a graphical, visual form, which is easier for a general understanding of the market situation than textual or digital information. They allow you to see the mass behavior of the crowd, as well as assess the balance of power between sellers and buyers, which ultimately makes it possible to understand the profitability potential of transactions.

Types of stock charts

There are three main types of graphical display of value - line, bar and candlestick. Each of these instruments provides information about the opening price of the corresponding period, the closing price, the lowest and highest prices (except for the line chart, which is built only on the basis of closing prices).

Charts used by traders show price changes over a specific time period, such as 1, 30, 60 minutes, a day, a week, a month or a year.

In fact, stock charts this is the story of the struggle between bulls and bears for dominance in the market. As a result of such a struggle, a huge number of transactions are made, each of which is necessarily reflected on the chart - one tick corresponds to one similar transaction. When the price rises, it means that someone is already suffering losses, and someone is already making money.

That is, in fact, stock charts are not just conditional reflection changes in value, and primarily show human emotions - fear and greed, despair and hope.

Japanese candlestick chart

This graph was invented by the Japanese rice trader Munehisa Homma in the 17th century and this moment is the most common method of displaying market data. Observing a regular price chart is not very convenient, so to build “Japanese candlesticks”, time is divided into periods, for example, 10 minutes. This division into periods makes the overall picture clear, which helps to judge the trend.

In our example, a chart for 1 day is selected and each of its divisions corresponds to 1 hour. Here, red and green rectangles (called jittai, Japanese for body) are colored depending on whether the opening price was lower than the period's closing price or vice versa.

How to read the YAS chart

The maximum and minimum prices are displayed as a vertical line in the body of the candle. Using the example, it is easy to see that on January 8, for 1 hour from 22 to 23 hours, the maximum rate was $958.21954, and the minimum was $922.84726.

In this case, we see that the hour began at a rate of $935.00001 per 1 BTC, and ended at a rate of $956.99000 per 1 BTC, so the rectangle is colored green.

The vertical line is called "kage" (shadow). Thanks to the shadows, similar to the wick of a candle, the chart got its name.

In practice, the relative length of the wicks can be used to judge the trend for the next period. A long upper part of the wick (compared to the lower) can indicate further growth, and a longer lower part can indicate a fall in the exchange rate.

1. volume,
2. time,
3. price.

Because analyzing trader charts comes down to calculating the balance of supply and demand. And the forces of supply and demand, according to the law of the same name, are expressed through price (vertical axis in the figure above) and volume (number of transactions, horizontal). By being able to read charts of volume and price over time, a trader can see changes in the balance of buyers and sellers, and take an advantageous position in advance before the price begins to change.

An example of reading and understanding a course chart

1. After the market opened, the price made a spring (a fraudulent downward maneuver, knocking down the stops of yesterday's bulls and dragging the bears into unprofitable sales).
2. A wave of purchases, locking sellers in the red. The green color on the volume histogram exceeds the red color - purchases occur at market price, a bullish sign.
3. Above the level of 80300, sot – shortening of the thrust – shortening of the breakthrough occurs. Each new high demonstrates a smaller and smaller increase in price on the chart. A sign that bears are resisting. The subsequent downward wave at 9:45 is further confirmation of this.
4. The blue arrow at 10:16 shows a candle on the chart when the efforts of buyers did not bring growth. And most likely, they displayed sellers meeting ask and above 80250 (also, by the way, sot)
5. The red arrow is a signal to enter a short position. In the background we have several bearish signs that justify shorting. And this candle with a predominant sales volume may indicate the beginning of a downward wave. A short is opened in the next 2-3 minutes, for example at 80100, with a stop at 80250, and a target at 79500 - the level where buyers showed their advantage, starting the morning upward wave.

Deal Potential: possible loss 150, possible profit 600. Ratio: 1:4 - a good ratio for a trade with a high probability of success.

To improve your market reading skill, cover the right side of the chart with paper, and open it by moving the paper to the right bar by bar. Record your conclusions with each open bar and try to understand the essence of the processes taking place.

Video lesson

For complete beginners in this matter, we suggest watching a short 3-minute training video. It gives a good idea and basic knowledge of deciphering crypto currency exchange rate charts.

Is it possible to make money on the stock exchange?

The famous trader, Richard Dennis, began trading on the stock exchange in the 70s with $1,600 borrowed and turned it into $200 million in 10 years. Dennis' strategy was radically different from what his competitors were doing. While other exchange players were engaged in “scalping”, that is, they made many operations in one day, trying to catch minor changes in the rate, Dennis held positions for long periods, trying to make money on trends (directions of price movement). So the answer to the question about the possibility of earning money is absolutely affirmative - yes, if you study and train. Successful trading on cryptocurrency exchanges!

Learning the basic skills needed to trade Forex, such as reading charts, is extremely important for a trader. This is because once you add this vital skill to your knowledge, it will be much easier when it comes time to learn and practice real forex trading.

You can't do without the basics

First, let's remember the basics of forex trading, because they are directly related to reading forex charts.

Every currency pair is always quoted in the same way. For example, the EUR/USD currency pair has a base currency of the euro - EUR and a minor currency of the dollar, and not vice versa. Therefore, the EUR/USD chart shows that the current price fluctuation is approximately 1.2155, which means that 1 euro can buy approximately 1.2155 US dollars.

And your trade size (notional value) is the amount of the base currency you are trading. In this example, if you want to buy 100,000 EURUSD, you buy 100,000 euros.

5 Basic Rules for Reading Forex Charts

1. If you buy a currency pair, that is, when you borrow, realize that you are expecting this currency pair to go up on the chart in order to make a profit on the trade. That is, you want the base currency to strengthen relative to the minor currency.

On the other hand, if you sell a currency pair from a short position, then you need the currency pair to go down on the chart to make a profit on the trade. So you want the base currency to weaken against the minor currency. So far everything is quite simple.

2. Always check the displayed time period. Many trading systems use different time frames to determine the entry point of a trade. For example, a system might use a four-hour or thirty-minute chart to determine the general direction of a currency pair using indicators such as , momentum or support and resistance lines, and then a five-minute chart to look for a rise after a temporary decline to determine the actual entry.

Therefore, you need to make sure that the graph you are considering has correct time frame for analysis. The best way to do this is to set the necessary time frames for the chart and indicators for the system in accordance with which you trade, in order to save and then reuse these settings.

3. Most forex charts display the bid price, not the ask price.. Remember that the price is always set with a bid and an ask (offer). For example, the current price of EURUSD could be 1.2055 bid and 1.2058 ask (or offer). When you buy, you do so at the ask price, which is the higher of the two spread prices, and when you sell, you do so at the bid price, which is the lower of the two prices.

If you are using a chart to determine entry and exit points, remember that when you place a sell order, when the price on the chart is 1.330, this is the price at which you will sell if there is no slippage.

On the other hand, you place a buy order when the price on the chart is the same, then you are actually buying at 1.3333. The trading system will often determine whether your orders will be placed simply according to the price on the chart, or whether you will need to add a buffer when buying or selling.

It should also be noted that on many platforms, when you place an order (to buy if the price rises relative to a certain price, or to sell if the price falls relative to a certain price), you can select either a “stop on bid” or “stop on offer” "

4. Remember that the times indicated at the bottom of the forex charts refer to specific time zones for which these charts were built, for example, GMT, New York time or others.

It can be handy to have a world time clock on hand so you can convert time between different time zones. This is especially important if you are trading in line with economic announcement releases.

You will need to convert the release time to your local time and chart time in order to know when the announcement will occur and therefore when you need to trade.

5. Finally, check does the time on your forex chart correspond to the opening of the candle or the closing of the candle. Your charting program may differ from other programs in this way.

If you want to trade major economic announcements, either by entering a trade based on changes following such announcements, or exiting a trade before an announcement to avoid getting knocked out in the process, then you need to be precise (to the minute!) as such transactions are made in accordance with what happens in the first minute after the announcement, and not a candle later!

You now have 5 key chart reading tips that will help you avoid common mistakes that many new forex traders make when reading charts. They will help you speed up the process of selecting a charting software package and trading systems that you want to use for Forex trading!

Knowing how to read charts is a key skill successful trader: If you decide to enter the cryptocurrency market, knowing the price is not enough to make trading decisions. A trader needs to fully understand what information a chart contains, and today we will learn how to do this.

There are three types of charts: a line chart, and a chart called “Japanese candlesticks”.

Line chart

This is the basic chart that a trader has to deal with - it is simply a change in the parameter of a particular cryptocurrency over time.

The chart can track various parameters of a cryptocurrency, such as its price or .

Using such a chart, you can judge the coins on the horizon of the month, week, day or even the last hour.

The chart above shows the price of Bitcoin in dollars. You can also use it to determine the opening price and closing price, as well as the lowest and highest price for the selected period.

A similar chart from popular price tracking site CoinMarketCap.com also provides insight into each coin, its price in dollars and bitcoins, and 24-hour trading volume.

bar chart

Histograms are very useful for cryptocurrencies and investors. They consist of vertical lines and small horizontal bars, and Ihodl.com uses two types of histograms - simple and color. Let's look at a color chart with green or red bars.

The top point of the vertical line here represents the highest, and the bottom - the lowest price for a certain period of time. The left line shows the opening price, and the right line shows the closing price.

"Japanese candles"

A candlestick chart, or candlestick chart, is also used to describe price movements of currencies or derivatives; Usually each candle is one day.

Steve Nison introduced such charts into Western business practice in his popular 1991 book, Candlesticks: Graphical Analysis financial markets».

These charts are the most popular among cryptocurrency traders. They are intended for advanced traders, but they are not difficult to understand.

Each "candle" on the chart shows the opening price, the lowest and highest price for a given period of time, and the closing price.

The size and color of the candle body and the length of the shadow or wick are very important as they demonstrate current trends as well as indicate reversals and future price movements.

The color of the candle indicates whether the closing price was higher than the opening price (usually green) or lower (usually red).

Wicks or shadows, that is, thin lines extending up or down from the body of the candle, show the lowest and highest prices for the selected period.

However, price analysis is only part of the task, because it is equally important to understand the reasons for sudden ups and downs. So do not forget, which can affect the state of the cryptocurrency market - if something significant happens, no charts will help predict the subsequent price jump.

If you are just starting to explore the world of cryptocurrencies, welcome to: everything a beginner needs to know about the cryptocurrency market and the basics of investing.

Subscribe to our channel in Yandex.Zen. Lots of exclusive stories, useful materials and beautiful photos.

Stock charts are one of the most important tools for analyzing current market situations and predicting future price behavior. They allow you to determine the balance of power between bulls and bears and make a choice in favor of those on whose side the majority is. In addition, a stock chart can help assess the growth (or fall) potential of the instrument being analyzed in order to make a decision about entering a trade. This is where the study of technical analysis begins.

There are currently three main types of charts used in stock trading:

• linear
• Japanese candles

Line graph

The simplest and most understandable type of presentation of stock quotes for beginners. These are the graphs that everyone drew at school and college. Points equal to the closing prices of the periods are plotted on the chart. And these marks are connected by lines. As a result, we get a similar picture.

Sometimes a line chart is displayed in a different form, when the entire space below the price is filled in with color. The picture below is similar to a linear graph, only in the form of an area.

A line graph is convenient for human perception, since it does not contain unnecessary information. Everything is extremely simple - the line goes up - an uptrend, falls - a downtrend. However, for a more serious analysis it lacks much additional information, which is why most traders use other types of charts.

Bars

A graphical representation of prices on a chart using bars is more informative. Unlike linear, bars additionally show opening prices, the maximum and minimum that the price reached in a given period.

The bar is a vertical line with horizontal segments on the right and left. Depending on the selected chart presentation interval, such data will be shown by one bar. If a daily interval is selected, then one bar is one day, a weekly one is 1 week, etc.

The length of the bar corresponds to the price range. The upper and lower points are the maximum and minimum quote levels, respectively. The line on the right is the opening price, on the left is the closing price. If the left line is lower than the right, then the closing price is higher than the opening price and we are seeing growth. And vice versa, when the left line is higher than the right, we get a closing price lower than the opening price and the market prices are falling.

Japanese candles

Japanese candlesticks carry absolutely identical information as bars, namely opening and closing prices, maximum and minimum quotes for the selected period. The difference between bars and candles is only in the graphical representation.

If bars are displayed as a horizontal line, then for candles the part between the opening and closing prices is drawn thicker. It is called the body of the candle. And the interval from the body of the candle to the high-low is the shadow of the candle.

In addition, depending on the rise or fall, the body of Japanese candlesticks is painted in different colors. In the classic version, white is growth, black is fall. Another common option: a combination of green and red colors, where red indicates a decrease in quotes, green indicates growth. Many traders use their own color combinations, but this is more a matter of habit.

Coloring improves the perception of the graph.

The same chart, presented in the form of Japanese candlesticks.

Using candles and bars in technical analysis

Example 2.

A candle referred to in Japanese analysis as a hammer. She talks about the following: when the market opened, the bears seized power and pushed the price down, but later their strength dried up and the majority sided with the bulls, who again raised the price up, almost to the opening prices. Therefore, there is a high probability of growth the next day.

Of course, a full analysis cannot be done based on just one candle. Usually their combinations are used, in conjunction with support and resistance lines, which give more high probability occurrence of predicted events in the future. Therefore, you need to correctly learn how to read stock charts to successful trading on the stock market.