Question

select the correct answer.

the graph of a parent function is shown.

which function belongs to the same function family as the graphed function?

\\(f(x) = \frac{1}{3x - 9}\\)

\\(f(x) = \frac{1}{3}\sqrt3{x} + 9\\)

\\(f(x) = 9x^3 + 2\\)

\\(f(x) = 9\log 2x\\)

Explanation:

Identify the parent function from the graph

$$ y = \sqrt[3]{x} $$

Match the parent function to its family

The graph represents a cube root function family.

Select the matching function from the options

$$ f(x) = \frac{1}{2}\sqrt[3]{x+9} $$

Answer:

• (A) \(f(x) = \frac{1}{2x-9}\)
• (B) \(f(x) = \frac{1}{2}\sqrt[3]{x+9}\) (Correct answer)
• (C) \(f(x) = 9x^3 + 2\)
• (D) \(f(x) = 9\log 2x\)