Chapter 3, Problem 5RE

(a)

To determine

To find: the slope and y-intercept of the given linear function.

Answer to Problem 5RE

Slope $m=0$ and $y$ intercept, $b=4$

Explanation of Solution

Given:

  $G(x)=4$

Calculation:

The slope intercept form of a line is $y=mx+c$

Where the slope of the line is $m$

And $y$ intercept is $b$ .

Compare the function $G(x)=0.x+4$ with slope intercept form.

Slope $m=0$ and $y$ intercept, $b=4$

Conclusion:

Therefore, the slope $m=0$ and $y$ intercept, $b=4$

(b)

To determine

To find: the average rate of change of the given function

Answer to Problem 5RE

The rate of change is 0

Explanation of Solution

Calculation:

For calculating average rate of change of function $G(x)=4$ , it is needed two points. $Y$ Intercept (0,4) is one point and for second point

Let $x=1$

  $G(1)=0\times 1+4$

  $\begin{array}{l}=0+4\hfill \\ =4\hfill \end{array}$

So second point in $(x,y)$ form is (1,4) .

Now as rate of change $\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

Here $x_1=0,y_1=4,x_2=1,y_2=4$

So rate of change $=\frac{4-4}{1-0}$

  $\begin{array}{l}=\frac{0}{1}\\ =0\end{array}$

Conclusion:

Therefore, the rate of change is 0

(c)

To determine

To graph: the given function.

Answer to Problem 5RE

  

Explanation of Solution

Calculation:

The line joining two points (0.4) and (1,4) is shown below where there is no $x$ intercept.

  

Conclusion:

Thus, the given function is drawn.

(d)

To determine

whether the function is increasing decreasing or constant.

Answer to Problem 5RE

The function is Constant in the interval $[-\infty ,+\infty ]$

Explanation of Solution

Calculation:

As the slope of the function $G(x)=4$ is 0, that means it is a constant function, parallel to $x$ axis.

Thus function is Constant in the interval $[-\infty ,+\infty ]$

Conclusion:

Thus function is Constant in the interval $[-\infty ,+\infty ]$