Question

pick the graph of the following function.

\\f(x) = (x-3)^3\\

Explanation:

Step1: Identify the parent function

The parent function is \(y = x^3\).

Step2: Determine the horizontal shift

The term \((x - 3)\) shifts the graph right by \(3\) units.

Step3: Find the inflection point

The inflection point shifts from \((0,0)\) to \((3,0)\).

Step4: Match with the correct graph

The top-right graph has its inflection point at \((3,0)\).

Answer:

The third graph (top right) is the correct graph of the function.