Question

The graph of f, of, x, equals, start fraction, minus, 1, divided by, x, end fractionf(x)= x −1 ​ is given below. Write the equation of a function g, of, xg(x) which would shift the graph of f, of, xf(x) right 3 units.

Answer 1

To shift the graph of the function \( f(x) = -\frac{1}{x} \) to the right by 3 units, you need to replace \( x \) in the function with \( x - 3 \).

The transformed function \( g(x) \) will be:

\[
g(x) = f(x - 3) = -\frac{1}{x - 3}
\]

So, the equation of the function \( g(x) \) which shifts the graph of \( f(x) = -\frac{1}{x} \) right by 3 units is:

\[
g(x) = -\frac{1}{x - 3}
\]