The function f(x)=x^2. The graph of g(x) is f(x) translated to the right 3 units and down 3 units. What is the function rule for g(x)?

Question

I honestly have no idea how to this… An example or helping me get through the problem would be great :) Thank you so much :)

Answer 1

to move up or down just add or subtract the constant equal to the units moved

so just to move it DOWN 3 would give us
g(x) = x^2 - 3

to move horizontally replace each x with (x ± c)
if you move it to the right, you need x - c
if you move it to the left , you need x + c

so , since we are moving 3 units to the right, we replace the x with x-3

g(x) = (x-3)^2 - 3

This should be in your notes or in your text.