Question

HEEEEEEEEELLLLLPPPPPP!!!!!!!

Susan started a small business and purchased a printer that cost $60. The function f represents her total printing costs after one year, where x is the cost of one ink cartridge.

f(x) = 15x + 60

Her brother Jason also started a business and purchased a printer. Including the cost of the printer, the function g represents his total printing costs after one year, where x is the cost of one ink cartridge.

When the two situations are represented by graphs, the graph of the second situation is the graph of the first situation, shifted up 12 units.

Determine the explicit function that defines the second situation.

CHOICES ARE
A. g(x) =15x + 72

B g(x) =180x +720

C g(x)=27x + 60

D g(x) =15x + 12

Answer 1

Option A is correct

`g(x) =15x+72`

Explanation:

Shifting up:

A parent function y =f(x),

To move a parent function b units up , you must add outside the function i.e,

y = f(x)+b

As per the statement:

Susan started a small business and purchased a printer that cost $60.

The function f represents her total printing costs after one year is:

f(x) = 15x + 60 ,where x is the cost of one ink cartridge.

It is also given that the function g represents his total printing costs after one year, where x is the cost of one ink cartridge.

When the two situations are represented by graphs as shown below

i.e

The graph of the second situation is the graph of the first situation, shifted up 12 units.

By definition we have;

⇒
`g(x) = f(x)+12`

Substitute the function f(x) we have;

`g(x) =15x+60+12`

⇒
`g(x) =15x+72`

Therefore, the explicit function that defines the second situation is:

`g(x) =15x+72`

Answer 2

To move a graph up, you need to add the units tot he end of the equation.

The graph of f(x) is f(x) = 15x+60

So add 12 to the equation to get g(x) = 15x +72

The answer would be A.