Chapter 1.3, Problem 32E

(a)

To determine

To sketch: the graph of the given function.

Explanation of Solution

Given information:

The function $f(x)=x$

Graph:

The given function is sketched as shown below.

  

Interpretation

From the graph, it can be seen that the given function is increasing linearly for all real values of x .

(b)

To determine

To find: the nature of the function from the graph and using a table of values of the function.

Answer to Problem 32E

The given function is an increasing function.

Explanation of Solution

Given information:

The function $f(x)=3$ .

From the graph of the function in previous part, it can be seen that, for all values of x from -8 to 8 , the value of f (x ) increases linearly. Thus, the given function is an increasing function over the interval (-8,8).

Now, the values of the given function for different values of x are shown in the below table.

  

From the table, it can be verified that, for increasing values of x , the function increases. Thus, $f(x)=x$ is an increasing function.