Question

which of the following statements is true about the function \\(y = \sqrt3{x} - 6\\)?

a. the parent function is shifted 6 units downward.
b. the parent function is shifted 6 units upward.
c. the parent function is shifted 6 units right.
d. the parent function is shifted 6 units left.

Explanation:

Identify the parent function

$$ f(x) = \sqrt[3]{x} $$

Analyze the transformation

$$ y = \sqrt[3]{x} - 6 = f(x) - 6 $$

Determine the shift direction

Subtracting \(6\) from the function value shifts the graph \(6\) units downward.

Answer:

• a. The parent function is shifted 6 units downward. (Correct answer)
• b. The parent function is shifted 6 units upward.
• c. The parent function is shifted 6 units right.
• d. The parent function is shifted 6 units left.