Chapter 1.2, Problem 79E

Solution

Part (a)

To find: sketch a graph.

The graph is

  

Given information:

The function $f$ is continuous for all $x$ .

Calculation:

A possible sketch is a line or a curve going from left to right. Draw the graph without lifting your pen.

  

Part (b)

To find: sketch a graph.

The graph is

  

Given information:

The function $f$ is increasing on $\left(-\infty ,0\right)$ and on $\left[3,5\right]\text{; }$

Calculation:

The graph should be increasing from left to right on the given intervals: $(-\infty ,0]$ and $\left[3,5\right]$ .

The other intervals, $\left[0,3\right]$ and $[5,\infty )$ can be constant or decreasing.

  

Part (c)

To find: sketch a graph.

The graph is

  

Given information:

The function $f$ is decreasing on $\left[0,3\right]$ and on $[5,\infty )\text{;}$

Calculation:

The graph should be decreasing from left to right on the given intervals: $\left[0,3\right]$ and $[5,\infty )$ .

The other intervals, $(-\infty ,0]$ and $\left[3,5\right]$ can be constant or decreasing.

  

Part (d)

To find: sketch a graph.

The graph is

  

Given information:

The function $\text{f}\left(\text{0}\right)\text{=f}\left(\text{5}\right)\text{=2}$ .

Calculation:

Two points on the graph should be $\left(0,2\right)$ and $\left(5,2\right)\text{: }$

  

Part (e)

To find: sketch a graph.

The graph is

  

Given information:

The function $f$ is decreasing on $\left[0,3\right]$ and on $[5,\infty )\text{;}$

Calculation:

A point on the graph should be $\left(3,0\right)\text{: }$