Question

fva 2s - 29: algebra ii q3
cubic and cube root functions and equations
the graph of the parent function $f(x) = x^3$ is translated to form $g(x) = (x - 2)^3 - 3$. which is the graph of $g(x)$, the translated function?

Explanation:

Step1: Identify parent function vertex

The parent function $f(x)=x^3$ has its inflection point (key vertex) at $(0,0)$.

Step2: Apply horizontal translation

For $g(x)=(x-2)^3-3$, the $(x-2)$ term shifts the graph 2 units right. The new x-coordinate of the vertex is $0+2=2$.

Step3: Apply vertical translation

The $-3$ term shifts the graph 3 units down. The new y-coordinate of the vertex is $0-3=-3$.

Step4: Match vertex to graph

The vertex of $g(x)$ is $(2,-3)$. The top-most graph has its inflection point at $(2,-3)$, matching the translated function.

Answer:

The top-most graph (first option)