Question

What transformation of the parent function f(x) is made to get 4f(x + 2)?

O

A. a vertical stretch by 4 and horizontal shrink by 1/2

O B. a vertical stretch by 4 and horizontal shrink by 2

O

C. a vertical stretch by 4 and 2 units in the x-direction

O

D. a vertical stretch by 4 and -2 units in the x-direction

Answer 1

Option D - a vertical stretch by 4 and -2 units in the x-direction

Explanation:

To find : What transformation of the parent function f(x) is made to get
`4f(x + 2)`?

Solution :

The parent function is f(x)

The transformed function is
`4f(x + 2)`

As 4 is multiplied by the function,

When f(x)→a f(x) a>1 then it stretch vertically by a factor of a.

So, there is a vertical stretch by 4.

As 2 is added in the function,

When f(x)→f(x+a) then it shift left or in -x direction by a factor of a.

So, there is a shift of -2 units in the x-direction.

Therefore, option D is correct.