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.

Step-by-step explanation:

The slope of this line = (y₂ - y₁) ÷ (x₂ - x₁)

                                   =  (2 - (- 1 )) ÷  (-6 - (-4))

                                   =  3 ÷ (-2)

                                   =  - ³/₂

The equation of the line can be determined using the point-slope form:

y - y₁ = m(x - x₁)

⇒ y - 2 = -³/₂(x - (-6))

   y - 2 = -³/₂ (x + 6)