Question

the graph of $f(x) = \frac{-2}{x}$ is given below. write the equation of a function $g(x)$ which would shift the graph of $f(x)$ right 5 units and down 4 units.

Explanation:

Step1: Recall horizontal shift rule

To shift a function \( f(x) \) right by \( h \) units, we replace \( x \) with \( x - h \) in the function. Here, \( h = 5 \), so we replace \( x \) with \( x - 5 \) in \( f(x)=\frac{-2}{x} \), getting \( \frac{-2}{x - 5} \).

Step2: Recall vertical shift rule

To shift a function down by \( k \) units, we subtract \( k \) from the function. Here, \( k = 4 \), so we subtract 4 from \( \frac{-2}{x - 5} \), resulting in \( g(x)=\frac{-2}{x - 5}-4 \).

Answer:

\( g(x)=\frac{-2}{x - 5}-4 \)