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 1 unit.

Explanation:

Step1: Recall horizontal shift rule

To shift a function \( f(x) \) right by \( h \) units, we replace \( x \) with \( x - h \). Here, \( h = 5 \), so for \( f(x)=\frac{2}{x} \), after horizontal shift, we get \( \frac{2}{x - 5} \).

Step2: Recall vertical shift rule

To shift a function down by \( k \) units, we subtract \( k \) from the function. Here, \( k = 1 \), so we subtract 1 from \( \frac{2}{x - 5} \). Thus, \( g(x)=\frac{2}{x - 5}-1 \).

Answer:

\( g(x)=\frac{2}{x - 5}-1 \)