Question

1. f(x)=(x + 2)^3

parent graph:
questions to ask: (circle answers) shift or flip or dilate? outside or inside? vertical or horizontal? expect or opposite?
transformation(s):

Explanation:

Step1: Identify parent - function

The parent function of $f(x)=(x + 2)^3$ is $y = x^3$.

Step2: Analyze transformation type

The $+2$ is inside the function (affecting the $x$ - value). For a function $y = f(x + h)$, when $h>0$, it is a horizontal shift. Here $h = 2$, so it is a horizontal shift.

Step3: Determine shift direction

For $y=f(x + h)$, the shift is in the opposite direction of the sign of $h$. Since $h = 2>0$, the graph of $y=x^3$ is shifted 2 units to the left.

Answer:

Parent Graph: $y = x^3$
Transformation(s): Horizontal shift 2 units to the left.