Question

the graph of g(x) is f(x) translated to the left 8 units and up 2 units. what is the function rule for g(x) given f(x)=x^2?

Answer 1

"translated to the left 8 units" implies Replace x by (x + 8)
"up 2 units" implies Add 2 to the right hand side.

Answer 2

g(x) = f(x+8) + 2
f(x) = x^2
g(x) = (x+8)^2 + 2

Answer 3

im lost :/

Answer 4

wait would that be the answer?

Answer 5

The g(x) function shown above is what we get after translating f(x).
IDK if they want just that or if they are expecting you to explain all the intermediate steps.

Answer 6

ooh okay. i honestly dont understand how you go g(x)=f(x+8)+2 though. can you please explain?

Answer 7

Sure.

You start with the graph of f(x).

If you now move this graph to the LEFT by 8 units, the equation of the graph will change from f(x) to f(x+8). So moving to the left means replace x by (x+8).
If you move the graph of f(x) to the RIGHT by 8 units, the equation of the graph will change from f(x) to f(x-8). So moving to the right means replace x by (x-8).

If you move the graph of f(x) UP by 2 units, the equation will change to f(x) + 2.
If you move the graph of f(x) DOWN by 2 units, the equation will change to f(x) - 2.

Answer 8

Here we move f(x) to the LEFT by 8 units. So it changes to f(x+8).
We then move it UP by 2 units which changes it to f(x+8) + 2
So f(x) = x^2 becomes
(x+8)^2 + 2 which is given a new name g(x)
g(x) = (x+8)^2 + 2

Answer 9

i get it now! thank you so much :)