Question

question the graph of $f(x) = 2x^3$ is given below. write the equation of a function $g(x)$ which would shift the graph of $f(x)$ down 3 units.

Explanation:

Step1: Recall Vertical Shift Rule

To shift a function \( y = f(x) \) down by \( k \) units, the new function is \( g(x)=f(x)-k \).

Step2: Apply the Rule to \( f(x) \)

Given \( f(x) = 2x^3 \) and we want to shift it down 3 units, so \( k = 3 \). Substitute into the formula: \( g(x)=2x^3 - 3 \).

Answer:

\( g(x) = 2x^3 - 3 \)