Answer:
b. [tex]g(x)=f(x)-5[/tex]
Step-by-step 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:
[tex]g(x)=f(x)+a[/tex] (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. [tex]g(x)=f(x)-5[/tex]
