Chapter 6.1, Problem 50PPS

(a).

To determine

Make a table showing values for $f(x),g(x),\left(f+g\right)(x),\left(f-g\right)(x)$

Explanation of Solution

Given:

Let $f(x)=x^2\text{ and }g(x)=x$ .

Calculation:

The table is :

We have

  $\begin{array}{l}f(x)=x^2\text{ and }g(x)=x\\ \Rightarrow \left(f+g\right)(x)=f(x)+g(x)=x^2+x\\ \Rightarrow \left(f-g\right)(x)=f(x)-g(x)=x^2-x\end{array}$

x	$f(x)=x^2$	$g(x)=x$	$\left(f+g\right)(x)=x^2+x$	$\left(f-g\right)(x)=x^2-x$
-3	9	-3	6	12
-2	4	-2	2	6
-1	1	-1	0	2
0	0	0	0	0
1	1	1	2	0
2	4	2	6	2
3	9	3	12	6

(b).

To determine

Graph $f(x),g(x),\left(f+g\right)(x)$ on the same coordinate grid

Explanation of Solution

Given:

Let $f(x)=x^2\text{ and }g(x)=x$ .

Calculation:

From part (a), we have:

  $\begin{array}{l}f(x)=x^2\text{ and }g(x)=x\\ \Rightarrow \left(f+g\right)(x)=f(x)+g(x)=x^2+x\end{array}$

x	$f(x)=x^2$	$g(x)=x$	$\left(f+g\right)(x)=x^2+x$
-3	9	-3	6
-2	4	-2	2
-1	1	-1	0
0	0	0	0
1	1	1	2
2	4	2	6
3	9	3	12

Plot the points on the coordinate plane:

  

(c).

To determine

Graph $f(x),g(x),\left(f-g\right)(x)$ on the same coordinate grid.

Explanation of Solution

Given:

Let $f(x)=x^2\text{ and }g(x)=x$ .

Calculation:

From part (a), we have:

  $\begin{array}{l}f(x)=x^2\text{ and }g(x)=x\\ \Rightarrow \left(f-g\right)(x)=f(x)-g(x)=x^2-x\end{array}$

x	$f(x)=x^2$	$g(x)=x$	$\left(f-g\right)(x)=x^2-x$
-3	9	-3	12
-2	4	-2	6
-1	1	-1	2
0	0	0	0
1	1	1	0
2	4	2	2
3	9	3	6

Plot the points on the coordinate plane:

  

(d).

To determine

Describe the relationship among the graphs of $f(x),g(x),\left(f+g\right)(x),\left(f-g\right)(x)$

Explanation of Solution

Given:

Let $f(x)=x^2\text{ and }g(x)=x$ .

Calculation:

Clearly , if $f(x)=x^2\text{ and }g(x)=x$ , then $\left(f+g\right)(x)$ is the sum of the functions f and g ; while $\left(f-g\right)(x)$ is the difference of the function g from f.