Question

question the graph of ( f(x) = |x| ) 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

For a function \( y = f(x) \), a vertical shift down by \( k \) units is given by \( y = f(x)-k \).

Step2: Apply the rule to \( f(x)=|x| \)

Here, we need to shift down by 2 units, so \( k = 2 \). Substituting into the rule, we get \( g(x)=|x|-2 \).

Answer:

\( g(x) = |x| - 2 \)