Chapter 10.2, Problem 3E

To determine

To match the function.

Answer to Problem 3E

Graph D

Explanation of Solution

Given information: $y=\sqrt[3]{x+2}$

Formula Used: Cube root function is the set of all real numbers

Calculation:

The domain of a cube root function is the set of all real numbers. Unlike a square root function which is limited to non-negative numbers, a cube root can use all real numbers because it is possible for three negatives to equal a negative.

Domain = All Real $\left(-\infty ,\infty \right)$

The range is set of values that correspond with the Domain.

So,

Range = $\left(-\infty ,\infty \right)$

  $y=\sqrt[3]{x+2}$

So, Cube both sides

  $y^3=x+2$

  $\begin{array}{ccc}x& -2& -1\\ y& 0& 1\end{array}$

So,

Graph D is correct.