Question

shifting the cube root function quick check
what is the effect on the graph of $f(x) = \sqrt3{x}$ when $f(x)$ is replaced by $f(x - 1)$? (1 point)
\bigcirc the graph shifts left.
\bigcirc the graph shifts down.
\bigcirc the graph shifts up.
\bigcirc the graph shifts right.

Explanation:

Step1: Recall Function Shift Rules

For a function \( y = f(x) \), the transformation \( y = f(x - h) \) shifts the graph horizontally. If \( h>0 \), it shifts right; if \( h<0 \), it shifts left.

Step2: Apply to Given Function

Here, \( f(x)=\sqrt[3]{x} \), and we replace \( f(x) \) with \( f(x - 1) \), so \( h = 1>0 \). Thus, the graph shifts right.

Answer:

The graph shifts right. (Corresponding option: The graph shifts right.)