Question

question the graph of $f(x) = \frac{1}{x}$ is given below. write the equation of a function $g(x)$ which would shift the graph of $f(x)$ down 2 units.

Explanation:

Step1: Recall vertical shift rule

For a function \( y = f(x) \), shifting down \( k \) units gives \( y = f(x)-k \).
Here, \( f(x)=\frac{1}{x} \) and \( k = 2 \).

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

Substitute into the rule: \( g(x)=f(x)-2=\frac{1}{x}-2 \).

Answer:

\( g(x)=\frac{1}{x}-2 \)