Question

Let f(x)=6xf(x)=6x. The graph of f(x)f(x) is transformed into the graph of g(x)g(x) by a vertical compression of 1/3 and a translation of 2 units up.
What is an equation for g(x)g(x)?

Answer 1

given: f(x)=6x

transformations: vertical compression of 1/3, translation of 2 units up.

g(x) = 1/3 f (x)

remember: f(x) = 6x

6/3 = 2

so, g(x) = 2(x)

now add 2 since you are transitioning up

your answer is: g(x) = 2(x)+2

(ik this is an old question, but I wanted to ad a clearer explination for ppl that still need help)

Answer 2

Vertical compression implies that you multiply the function by a scalar or constant.
---> (1/3)*f(x)

Translating up means you are adding to the y-value or shifting the graph up.
----> f(x) + 2

Put it together and you get:
$g(x) = \frac{1}{3}f(x) + 2$
Now replace f(x) with 6x
$g(x) = \frac{1}{3} (6x) + 2 = 2x + 2$