Question

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 \( y = f(x) \), a vertical shift down by \( k \) units is given by \( y = f(x)-k \).
Here, \( f(x)=x^3 \) and \( k = 5 \).

Step2: Apply the shift rule

Substitute \( f(x) \) and \( k \) into the formula. So \( g(x)=f(x)-5=x^3 - 5 \).

Answer:

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