Question

describe the transformations and select the appropriate parent function.
select all that apply.
$y = -\sqrt3{x - 9} + 2$
□ shifts up 2
□ shifts down 2
□ shifts left 9
□ shifts right 9
□ vertically stretches by a factor of 2
□ vertically compresses by a factor of 1/2
□ reflects over the x-axis
□ cubic function
□ cube root function

Explanation:

Step1: Identify parent function

Parent function: $y=\sqrt[3]{x}$ (Cube Root Function)

Step2: Analyze horizontal shift

$x$ becomes $x-9$: shifts right 9

Step3: Analyze reflection

Negative sign outside $\sqrt[3]{x-9}$: reflects over x-axis

Step4: Analyze vertical shift

Add 2 to the expression: shifts up 2

Step5: Eliminate incorrect options

No vertical stretch/compress; no left/down shift; not cubic function.

Answer:

Shifts up 2, Shifts right 9, Reflects over the x-axis, Cube Root Function