Question

describe the transformations and select the appropriate parent function.
select all that apply.
$y = -4(x + 2)^3$
$square$ shifts up 2
$square$ shifts down 2
$square$ shifts left 2
$square$ shifts right 2
$square$ vertically stretches by a factor of 4
$square$ vertically compresses by a factor of 1/4
$square$ reflects over the x-axis
$square$ cubic function
$square$ cube root

Explanation:

Step1: Identify parent function

The parent function is $y=x^3$, a cubic function.

Step2: Analyze horizontal shift

For $y=(x+h)^3$, $h=2$ means shift left 2.

Step3: Analyze vertical stretch

The coefficient $4$ outside the term means vertical stretch by 4.

Step4: Analyze reflection

The negative sign $-4$ reflects over the x-axis.

Answer:

• Shifts left 2
• Vertically Stretches by a factor of 4
• Reflects over the x-axis
• Cubic Function