Question

the graph of $f(x) = -x^3$ is given below. write the equation of a function $g(x)$ which would shift the graph of $f(x)$ down 5 units.

Explanation:

Step1: Recall vertical shift rule

For a function \( y = f(x) \), shifting it down by \( k \) units (where \( k>0 \)) gives \( y = f(x)-k \).

Step2: Apply the rule to \( f(x)=-x^3 \)

We need to shift \( f(x) \) down 5 units, so \( k = 5 \). Substitute into the rule: \( g(x)=f(x)-5=-x^3 - 5 \).

Answer:

\( g(x)=-x^3 - 5 \)