Which of the following equations corresponds to the function represented in the table? <path fill="none" stroke="#616161" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-opacity=".8" stroke-width="2.5" d="M393.8 171.61v299.554M543.577 171.61v299.554M244.023 171.61v299.554M244.023 471.164h898.66M244.023 171.61h898.66M693.353 171.61v299.554M843.13 171.61v299.554M244.023 321.387h898.66M992.907 171.61v299.554M1142.683 171.61v299.554" paint-order="fill stroke markers"> X Y -1 2 5 8 11 2 4 6 8 10

$$ y=\frac{2}{3}x+2\frac{2}{3} $$

Graphical Representation of a Function

As we learned in an article on functions, the standard "correspondence rule" is a connection between a dependent variable $(Y)$ and an independent variable $(X)$ .

By means of a graph or drawing, which gives a visual aspect to the concept of the function. From the graph it is possible to understand whether it is a linear function (straight line), a quadratic function (parabola) and more.

Remember that when it comes to a graphical representation of a function, each point in the domain $X$ will always have only one point within the range $Y$ . Therefore, not every drawing is a graphical representation of a function. Here is an example.

A1 - Graphical representation of a function

Detailed explanation

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Test yourself on representations of functions!

Determine whether the given graph is a function?

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If you are interested in more information about "graphs" you can find detailed information in the following articles:

Graphical representation of a function

Collecting and Organizing Data - Statistical Research

Reading information from graphs

Graphing

Discrete graph

Continuous graph

Functions for seventh grade

In Tutorela you will find a variety of articles with interesting explanations about mathematics.

Exercises on the graphical representation of a function

Exercise 1

Task

Given the function:

$x=y-4+2x$

Through which of the following points does the graph of the function pass?

Solution

$x=y-4+2x$

$y=x-2x+4$

$y=-x+4$

$-1\cdot\left(-1\right)+4=5$

Answer

$\left(-1,5\right)$

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Test your knowledge

Question 1

Is the given graph a function?

Question 2

Does the graph below represent a function?

Question 3

Determine whether the following table represents a function

Exercise 2

Task

Given the line whose slope is $6$ and passes through the point $(6,41)$ .

Which of the algebraic representations corresponds to the given line?

Solution

$y=mx+b$

$m=6$

$\left(6,41\right)$

Replace accordingly

$41=6\cdot6+b$

$41-36=5=b$

$y=6x+5$

$y=2\left(3x+2\frac{1}{2}\right)$

Answer

$y=2\left(3x+2\frac{1}{2}\right)$

Exercise 3

Task

Given the line whose slope is $2$ and passes through the point $(3,7)$ .

Which of the algebraic representations corresponds to the given line?

Solution

$y=mx+b$

$m=2$

$\left(3,7\right)$

Replace accordingly

$7=2\cdot3+b$

$7=6+b$

$1=b$

$y=2x+1$

Answer

$y=2x+1$

Do you know what the answer is?

Question 1

Determine whether the following table represents a constant function:

Question 2

Determine whether the data in the following table represent a constant function

Question 3

Determine whether the following table represents a function

Exercise 4

Task

Given the straight line parallel to another straight line

$y=2x+5$

passing through the point $(4,9)$

Which of the algebraic representations corresponds to the given line?

Solution

$y=2x+5$

Parallel to the line

$m=2$

$\left(4,9\right)$

Replace accordingly

$9=2\cdot4+b$

$9=8+b$

$1=b$

$y=2x+1$

Answer

$y=2x+1$

Exercise 5

Task

Choose the correct answer

a.The graph passes through $(3,5)$

b.The graph passes through $(3,7)$

c.The graph passes through $(5,4)$

d.The graph passes through $(-1,6)$

Answer

The correct answer is a. The graph passes through $(3,5)$

Check your understanding

Question 1

Determine whether the following table represents a function

Question 2

Is the given graph a function?

Question 3

Is the given graph a function?

Review questions

What is a graphical representation of a function?

As we know a function can be represented in different ways: verbally, algebraically, table of values and graphically. The last representation means that a function can be graphed in the Cartesian plane, according to the values obtained in the table, this representation can be observed as a straight line, a parabola, among others, depending on the type of function we are working on.

How is a function represented graphically?

Let's see an example of how a function should be represented graphically.

Example:

Represent the following function in a graph

Task

Graph the following function $Y=X-1$

Solution

We are going to give values to $X$ , to find the value of $Y$ , according to the correspondence rule, and we are going to register these values in a table:

First, we are going to input the values of $X$ To get the values that correspond to $Y$ , the algebraic expression of this function is:

$Y=X-1$

Then,

When $X=-4$

$Y=-4-1=-5$

When $X=-3$

$Y=-3-1=-4$

When $X=-1$

$Y=-1-1=-2$

When When $X=0$

$Y=0-1=-1$

When $X=2$

$Y=2-1=1$

When $X=5$

$Y=5-1=4$

According to this data now we are going to input it in the table

Once we have the values in the table, we are going to look for these pairs of coordinates in the Cartesian plane, where we are going to find points and connect them as follows to obtain the final graph of the function

Graph:

According to these points that were located in the Cartesian plane, we can observe that a straight line was drawn, which means that the function is linear.

What are the types of graphical representation of a function?

There are many graphs of functions, this is according to the type of function that is being graphed, among the most common are:

Graph of a constant function

Graph of a linear function

Graph of a quadratic function

Graph of a cubic function

Graph of an exponential function

Do you think you will be able to solve it?

Question 1

Is the given graph a function?

Question 2

Is the given graph a function?

Question 3

Which of the following equations corresponds to the function represented in the graph?

Examples with solutions for Graphical Representation of a Function

Exercise #1

Determine whether the given graph is a function?

Video Solution

Step-by-Step Solution

It is important to remember that a function is an equation that assigns to each element in domain X one and only one element in range Y

We should note that for every X value found on the graph, there is one and only one corresponding Y value.

Therefore, the graph is indeed a function.

Answer

Yes

Exercise #2

Is the given graph a function?

Video Solution

Step-by-Step Solution

It is important to remember that a function is an equation that assigns to each element in domain X one and only one element in range Y

Let's note that in the graph:

$f(0)=2,f(0)=-2$

In other words, there are two values for the same number.

Therefore, the graph is not a function.

Answer

Exercise #3

Does the graph below represent a function?

Video Solution

Step-by-Step Solution

It is important to remember that a function is an equation that assigns to each value in domain $x$ only one value in range $y$ .

Since we can see that for every $x$ value found on the graph there is only one corresponding $y$ value, the graph is indeed a function.

Answer

Yes

Exercise #4

Determine whether the following table represents a function

Video Solution

Step-by-Step Solution

It is important to remember that a constant function describes a situation where as the X value increases, the function value (Y) remains constant.

In the table, we can observe that there is a constant change in X values, meaning an increase of 1, and a constant change in Y values, meaning an increase of 3

Therefore, according to the rule, the table describes a function.

Answer

Yes

Exercise #5

Determine whether the following table represents a constant function:

Video Solution

Step-by-Step Solution

It is important to remember that a constant function describes a situation where, as the X value increases, the Y value remains constant.

In the table, we can see that there is a constant change in the X values, specifically an increase of 2, while the Y value remains constant.

Therefore, the table does indeed describe a constant function.

Answer

Yes, it does

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