Question

Identify the parent function for the function g (x) = (x + 1)^3 based on its function rule. Then graph g and identify what the transformation of the parent function it represents.

Answer 1

Answer: $Cubic;\text{ translation left 1 unit \lparen3rd option\rparen}$

Explanation:

Given:

$g(x)\text{ = \lparen x + 1\rparen}^3$

To find:

the parent function

The highest degree of x is 3. The function will be cubic.

To determine the translation, we will apply the transformation rule:

$\begin{gathered} The\text{ parent function:} \\ y\text{ = x}^3 \\ \\ Transformation\text{ rule:} \\ f(x\text{ - d\rparen: translation to the right d units} \\ f(x\text{ + d\rparen: translation to the left d units} \end{gathered}$$\begin{gathered} g(x)\text{ = \lparen x + 1\rparen}^3 \\ This\text{ means a translation of 1 units to the left} \\ \\ Cubic;\text{ translation left 1 unit \lparen3rd option\rparen} \end{gathered}$