Question

a parent function and transformed function are shown:
\\y = \sqrt3{x}\\
\\y = -(0.4)\sqrt3{x - 2}\\

which of the following describes the graph of the transformed function compared with the parent function? select all that apply.

• reflected over the \\(x\\)-axis
• translated 2 units left
• translated 2 units right
• compressed by a factor of 0.4
• stretched by a factor of 0.4
• translated 2 units up
• translated 2 units down

Explanation:

Identify the transformation components

Using the Cube Root Transformations knowledge point

$$ y = a\sqrt[3]{x - h} + k $$

Comparing the parent function \(y = \sqrt[3]{x}\) with the transformed function \(y = -(0.4)\sqrt[3]{x - 2}\), we identify:

$$ a = -0.4,\quad h = 2,\quad k = 0 $$

Analyze the horizontal translation

Using the Horizontal Translation knowledge point

$$ h = 2 \implies \text{translated 2 units right} $$

Analyze the vertical dilation and reflection

Using the Function Reflections and Vertical Dilation knowledge points

$$
LATEXBLOCK0
$$

Answer:

• reflected over the x-axis (Correct answer)
• translated 2 units left
• translated 2 units right (Correct answer)
• compressed by a factor of 0.4 (Correct answer)
• stretched by a factor of 0.4
• translated 2 units up
• translated 2 units down