the basic graph of f(x) = 1/x is shown. manipulate the graph of f(x) to display the graph of g(x) = 1/(x +…

Explanation:

Step1: Identify horizontal shift

For the function $g(x)=\frac{1}{x + 4}-5$, compared to $f(x)=\frac{1}{x}$, the $x$ in the denominator is replaced with $x + 4$. According to the rule of function - graph transformation $y = f(x + h)$ is a horizontal shift of $y = f(x)$ by $h$ units. Here $h=-4$, so the graph of $f(x)$ is shifted 4 units to the left.

Step2: Identify vertical shift

The $- 5$ outside the fraction in $g(x)=\frac{1}{x + 4}-5$ means that according to the rule $y = f(x)+k$ is a vertical shift of $y = f(x)$ by $k$ units. Here $k = - 5$, so the graph of $\frac{1}{x+4}$ is shifted 5 units down.

Answer:

Shift the graph of $f(x)=\frac{1}{x}$ 4 units to the left and 5 units down.