Chapter 7.2, Problem 56E

a.

To determine

To find: The interval where graph of $y=\frac{a}{x}$ is increasing or decreasing when $a>0$ .

Answer to Problem 56E

Decreasing: $\left(-\infty ,\infty \right)-\left\{0\right\}$

Explanation of Solution

Given: $y=\frac{a}{x}$

The given function, $y=\frac{a}{x}$ .

This is inverse function and nature of graph depends on the sign of a .

Here, $a>0$

  

So, graph in decreasing in domain.

Decreasing: $\left(-\infty ,\infty \right)-\left\{0\right\}$

b.

To determine

To find: The interval where graph of $y=\frac{a}{x}$ is increasing or decreasing when $a<0$ .

Answer to Problem 56E

Increasing: $\left(-\infty ,\infty \right)-\left\{0\right\}$

Explanation of Solution

Given: $y=\frac{a}{x}$

The given function, $y=\frac{a}{x}$ .

This is inverse function and nature of graph depends on the sign of a .

Here, $a<0$

  

So, graph in increasing in domain.

Increasing: $\left(-\infty ,\infty \right)-\left\{0\right\}$