Agym offers three levels of membership based on the number of visits per month, as represented by the table.
which graph represents the total monthly cost at the gym as a function of the number of visits in a month?

The graph that represents the total monthly cost at the gym as a function of the number of visits in a month is shown by option A) and this can be determined by forming the linear equation.

Given :

A gym offers three levels of membership based on the number of visits per month.

Let the number of visits per month be 'a' and the total cost be 'b'. The correct graph that represents the total monthly cost at the gym as a function of the number of visits in a month will be:

A) For the interval of a = [0,12]

The value of b is given by:

b = 5a + 15

First, put the value of a = 0 in the above equation.

b = $15

Now, put the value of a = 12 in the above equation.

b = 60 + 15

b = $75

The interval of b = [15,75]

B) For the interval of a = [12,16]

The value of b is given by:

b = 4a + 32

First, put the value of a = 12 in the above equation.

b = 48 + 32

b = $80

Now, put the value of a = 16 in the above equation.

b = 64 + 32

b = $96

The interval of b = [80,96]

C) For the interval of a = [16,24]

The value of b is given by:

b = 3a + 42

First, put the value of a = 16 in the above equation.

b = 48 + 42

b = $90

Now, put the value of a = 24 in the above equation.

b = 72 + 42

b = $114

The interval of b = [90,114]

Therefore, the correct graph is shown in option A).

For more information, refer to the link given below:

link

The graph in the attached figure    

Step-by-step explanation:

Let

x > the number of visit per month

y > the total cost

we know that

Observing the table

1) For the interval of x equal to > [0,12]  (close circle both points)

The domain is all whole numbers greater than or equal to 0 visits and less than or equal to 12 visits

The value of y is

y=5x+15

For x=0 > y=$15

For x=12 > y=5(12)+15=$75

The range is the interval > [15,75] (close circle both points)

All real numbers greater than or equal to $15 and less than or equal to $75

2) For the interval of x equal to >(12,16] (open circle at left and close circle at right)

The domain is all whole numbers greater than 12 visits and less than or equal to 16 visits

The value of y is

y=4x+32

For x=12 > y=4(12)+32=$80

For x=16 > y=4(16)+32=$96

The range is the interval > (80,96] (open circle at left and close circle at right)

All real numbers greater than $80 and less than or equal to $96      

3) For the interval of x equal to >(16,24] (open circle at left and close circle at right)

The domain is all whole numbers greater than 16 visits and less than or equal to 24 visits

The value of y is

y=3x+42

For x=16 > y=3(16)+42=$90

For x=24 > y=3(24)+42=$114

The range is the interval > (90,114] (open circle at left and close circle at right)

All real numbers greater than $90 and less than or equal to $114    

therefore

The graph in the attached figure