# Representing a Function Verbally and with Tables - Examples, Exercises and Solutions

Function, describes a correlation or coincidence between a dependent variable ($Y$) and an independent variable ($X$). The legitimacy of this relationship between the variables is called the " correspondence rule ".

## Verbal representation of a function

The verbal representation of a function expresses the connection between variables verbally, i.e. through a story.

A typical verbal representation of a function can look like this:

• Assuming that Daniel reads all the books he buys that month, the total number of books Daniel reads per year ($Y$) is a function of the number of books Danny buys each month ($X$).

#### Tabular representation of a function

A tabular representation of a function is a demonstration of the legitimacy of a function using a table of values $X$ (independent variable) and the corresponding values $Y$ (dependent variable).

In general, a table of values is shown as follows:

## Examples with solutions for Representing a Function Verbally and with Tables

### Exercise #1

Is the given graph a function?

### 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.

No

### Exercise #2

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

### Step-by-Step Solution

Use the formula for finding slope:

$m=\frac{y_2-y_1}{x_2-x_1}$

We take the points:

$(0,-2),(-2,0)$

$m=\frac{-2-0}{0-(-2)}=$

$\frac{-2}{0+2}=$

$\frac{-2}{2}=-1$

We substitute the point and slope into the line equation:

$y=mx+b$

$0=-1\times(-2)+b$

$0=2+b$

We combine like terms:

$0+(-2)=b$

$-2=b$

Therefore, the equation will be:

$y=-x-2$

### Answer

$y=-x-2$

### Exercise #3

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

### Step-by-Step Solution

We will use the formula for finding slope:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let's take the points:

$(-1,4),(3,8)$

$m=\frac{8-4}{3-(-1)}=$

$\frac{8-4}{3+1}=$

$\frac{4}{4}=1$

We'll substitute the point and slope into the line equation:

$y=mx+b$

$8=1\times3+b$

$8=3+b$

Let's combine like terms:

$8-3=b$

$5=b$

Therefore, the equation will be:

$y=x+5$

### Answer

$y=x+5$

### Exercise #4

Is the given graph a function?

No

### Exercise #5

Is the given graph a function?

No

### Exercise #6

Determine whether the following table represents a function

No

### Exercise #7

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

No

### Exercise #8

Is the given graph a function?

Yes

### Exercise #9

Is the given graph a function?

Yes

### Exercise #10

Is the given graph a function?

Yes

### Exercise #11

Is the given graph a function?

Yes

### Exercise #12

Determine whether the following table represents a function

Yes

### Exercise #13

Determine whether the following table represents a function

Yes

### Exercise #14

Determine whether the following table represents a function

Yes

### Exercise #15

Determine whether the following table represents a function

No