Chapter 3.5, Problem 27E

Solution

To find the correct option: The equation of the translated graph,where the function of the shifted to $-2$ unit left . $y=3\sqrt[3]{x}$ .

  $A).y=3\sqrt[3]{x-2}B).3\sqrt[3]{x}-2C).3\sqrt[3]{x+2}D).3\sqrt[3]{x}+2$

The correct option is option $C$ .

Given information:

The given function is $y=3\sqrt[3]{x}$ .

Concept used:

If graph $y=af\left(x-h\right)+k$ is the transformed graph of parent function $y=f\left(x\right)$ then $k$ is positive then graph is vertical upward and $k$ is negative the graph will be vertically downwards by the factor $k$ .Also if h is positive graph translated to right and negative it will translated to left by the factor h. Similarly if $a$ is positive it is vertically stretched by the factor $a$ and negative it will vertical stretched and reflected to $x$ axis.

Explanations:

Here the parent function is $y=3\sqrt[3]{x}$ and the graph is shifted to left by the factor $-2$ means here $h=-2$ then equation of the translated graph will be $y=3\sqrt[3]{x+2}$ .

Hence the correct option is option $C$ .