Chapter 1.4, Problem 80E

a.

To determine

To identify:

Intervals on graph is increasing and decreasing of $y=-f\left(x\right)$

Answer to Problem 80E

Intervals on graph is increasing and decreasing of $y=-f\left(x\right)$ is:

Increasing: $\left(-2,1\right)$

Decreasing: $\left(-\infty ,-2\right)$ and $\left(1,\infty \right)$ .

Explanation of Solution

Give information:

Given function:

  $y=-f\left(x\right)$ .

  

Calculation:

The graph of $y=-f\left(x\right)$ is get by reflecting the graph of $f\left(x\right)$ about $x-$ axis. Then reflecting the given graph, intervals on which $y=-f\left(x\right)$ is increasing or decreasing are:

Increasing: $\left(-2,1\right)$

Decreasing: $\left(-\infty ,-2\right)$ and $\left(1,\infty \right)$ .

b.

To determine

To identify:

Intervals on graph is increasing and decreasing of $y=f\left(x\right)-3$

Answer to Problem 80E

Intervals on graph is increasing and decreasing of $y=f\left(x\right)-3$ is:

Increasing: $\left(-\infty ,-2\right)$ and $\left(1,\infty \right)$ .

Decreasing: $\left(-2,1\right)$ .

Explanation of Solution

Give information:

Given function:

  $y=f\left(x\right)-3$ .

  

Calculation:

The graph of $y=f\left(x\right)-3$ is get by shifting the graph of $y=f\left(x\right)-3$ units downwards.

The sifting the given graph $3$ units downwards do not change the intervals in which the graph of $f\left(x\right)$ is increasing or decreasing so the intervals on which $y=f\left(x\right)-3$ is increasing or decreasing are:

Increasing: $\left(-\infty ,-2\right)$ and $\left(1,\infty \right)$ .

Decreasing: $\left(-2,1\right)$ .

c.

To determine

To identify:

Intervals on graph is increasing and decreasing of $y=f\left(x-1\right)$

Answer to Problem 80E

Intervals on graph is increasing and decreasing of $y=f\left(x-1\right)$ is:

Increasing: $\left(-\infty ,-1\right)$ and $\left(2,\infty \right)$

Decreasing: $\left(-1,2\right)$ .

Explanation of Solution

Give information:

Given function:

  $y=f\left(x-1\right)$ .

  

Calculation:

The graph of $y=f\left(x-1\right)$ is get by shifting the graph of $f\left(x\right)1$ unit to the right.

Then shifting of the given graph $1units$ to right will change the intervals, so the intervals on which $y=f\left(x-1\right)$ is increasing or decreasing are:

Increasing: $\left(-\infty ,-1\right)$ and $\left(2,\infty \right)$

Decreasing: $\left(-1,2\right)$ .