# Graphical Representation of a Function

🏆Practice function representation

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

## Test yourself on function representation!

Is the given graph a function?

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

Graphing

Discrete graph

Continuous graph

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

## Exercises on the graphical representation of a function

### Exercise 1

Given the function:

$x=y-4+2x$

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

Solution

$x=y-4+2x$

$y=x-2x+4$

$y=-x+4$

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

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

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### Exercise 2

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

$41=6\cdot6+b$

$41-36=5=b$

$y=6x+5$

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

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

### Exercise 3

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

$7=2\cdot3+b$

$7=6+b$

$1=b$

$y=2x+1$

$y=2x+1$

Do you know what the answer is?

### Exercise 4

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

$9=2\cdot4+b$

$9=8+b$

$1=b$

$y=2x+1$

$y=2x+1$

### Exercise 5

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 $(-1,6)$

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

## 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

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?
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