Question

Let f(x)=(x+2)2.

Let g(x)=3(x+2)2.

Which statement describes the graph of g(x) with respect to the graph of f(x)?

A. It is stretched vertically by a factor of 3.
B. It is compressed horizontally by a factor of 3.
C. It is translated up 3 units
D. It is translated right 3 units.

Answer 1

Since you are essentially multiply the y value of f(x) by 3, you are stretching it vertically by a factor of 3.

Answer 2

A. It is stretched vertically by a factor of 3.

Explanation:

Given are two functions

f and g

`f(x) = (x+2)^2`

i.e. f is a parabola with vertex at (-2,0) open up

`g(x) = 3(x+2)^2`

This is also a parabola with vertex at (-2,0) open up

g(x) = 3 f(x)

This means f(x) is smaller vertically than g(x)

Or f(x) is stretched vertically by a factor of 3 to get g(x)

Hence option A is true.

A. It is stretched vertically by a factor of 3.