Question

The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)

Answer 1

Answer: g(x) = f(x) - 5

Explanation:

just took this

Answer 2

b.
`g(x)=f(x)-5`

Explanation:

You have that the function f(x) has its y-intercept for y=3.

Furthermore, you have that g(x) is a transformation of f(x) with y-intercept for y=-2.

In this case you have that f(x) has been translated vertically downward.

The general way to translate a function vertically in the coordinate system is:

`g(x)=f(x)+a` (1)

being a positive or negative.

if g(x) has its y-intercept for y=-2, and the y-intercept of f(x) is for y=3, then the value of a in the equation (1) must be a = -5, which is the difference between both y-intercepts, in fact:

a = -2 -3 = -5

Then, the answer is:

b.
`g(x)=f(x)-5`