Question

the graph of $y = \sqrt3{x}$ is shown below.which of the following is the graph of $y = 3\sqrt3{x + 6}$?choose 1 answer:

Explanation:

Step1: Identify base function transformation

Base function: $y=\sqrt[3]{x}$. Target: $y=3\sqrt[3]{x+6}$

Step2: Apply horizontal shift

Shift left 6 units: $y=\sqrt[3]{x+6}$

Step3: Apply vertical stretch

Stretch by factor 3: $y=3\sqrt[3]{x+6}$

Step4: Locate key point

Base key point $(0,0)$ becomes $(-6, 0)$ after shift, then $(-6,0)$ remains (stretch doesn't change x-intercept). At $x=2$, $y=3\sqrt[3]{8}=6$, so curve passes $(-6,0)$ and rises with vertical stretch.

Answer:

B. <The graph that shifts left 6 units and has vertical stretch by 3, passing through (-6,0) and rising to (2,6)>