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

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

Step-by-step explanation:

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

Solution :

The parent function is f(x)

The transformed function is

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.

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step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get