Question

The graph of function g is a vertical stretch of the graph of function f ​​by a factor of 3. Which equation describes function g?

A. g(x)=3f(x)
​​B. g(x)=f(3x)
​​C. g(x)=f(x3)
D.​​ g(x)=13f(x)

What transformation takes the graph of f(x)=3x+8 to the graph of g(x)=3x+6 ?
A. translation 2 units up
B. translation 2 units left
C. translation 2 units down
D. translation 2 units right

Answer 1

I did not have the answer to the second question but here is the first.

Answer 2

Explanation:

A vertical stretch by a factor of k means that the point (x, y) on the graph of f (x) is transformed to the point (x, ky) on the graph of g(x), where k <1.

If k =1, then same graph we obtain and if k>1 we get a vertically shrink graph.

In our question, there is a vertical stretch of 3. This means new graph would have points as (x,y/3)

i.e. instead of f(x) = y, we have now f(x) = y/3

So transformation is g(x) = 3f(x)

Option A is correct.

2) Here f(x) = 3x+8 is transformed to g(x) =3x+6

i.e. y intercept is reduced by 2 units. Hence there is a translation of 2 units down.