Chapter 2, Problem 26RE

(a)

To determine

To find: the domain and the range of $g$ .

Answer to Problem 26RE

The domain is

  $\left\{x|-5\le x\le 4\right\}$

The range is

  $\left\{y|-3\le y\le 1\right\}$

Explanation of Solution

Given information:

The graph of the function $g$ shown:

  

Calculation:

From the graph given in question $x\ge -5$ and $x\le 4$ . Hence the domain is

  $\left\{x|-5\le x\le 4\right\}$ . Also $y\ge -3$ and $y\le 1$ . Hence the range is

  $\left\{y|-3\le y\le 1\right\}$

(b)

To determine

To find: value of $g\left(-1\right)$ .

Answer to Problem 26RE

  $g\left(-1\right)=1$

Explanation of Solution

Given information:

The graph of the function $g$ shown:

  

Calculation:

From the given in question $\left(-1,1\right)$ lies on the graph, Hence

  $g\left(-1\right)=1$

(c)

To determine

To list: the intercepts.

Answer to Problem 26RE

The $x$ intercepts: $\left(0,0\right),\left(0,4\right)$ .

The $y$ intercept: $\left(0,0\right)$ .

Explanation of Solution

Given information:

The graph of the function $g$ shown:

  

Calculation:

From the graph given in question that $\left(0,0\right)$ and $\left(4,0\right)$ lie on the graph, Hence

The $x$ intercepts: $\left(0,0\right),\left(0,4\right)$ .

The $y$ intercept: $\left(0,0\right)$ .

(d)

To determine

To find: the value of $x$ when $g\left(x\right)=-3$ .

Answer to Problem 26RE

  $x=3$

Explanation of Solution

Given information:

The graph of the function $g$ shown:

  

Calculation:

From the graph given in question that $\left(3,-3\right)$ lies on the graph, Hence

  $g\left(3\right)=-3$ . Hence $x=3$

(e)

To determine

To solve: $g\left(x\right)>0$ .

Answer to Problem 26RE

  $\left\{x|-5\le x<0\right\}$

Explanation of Solution

Given information:

The graph of the function $g$ shown:

  

Calculation:

From the graph that $g\left(x\right)>0$ , when $x\ge -5$ and $x<0$ .

Hence the solution set is

  $\left\{x|-5\le x<0\right\}$

(f)

To determine

To sketch: the graph of $y=g\left(x-2\right)$ .

Explanation of Solution

Given information:

The graph of the function $g$ shown:

  

Calculation:

The following points lie on the graph of $y=g\left(x-2\right)$ .

  $\left(-3,1\right),\left(1,1\right),\left(2,0\right),\left(5,-3\right)$ and $\left(6,0\right)$ . The above points are plotted below using Maple.

The graph is a horizontal shift to right by 2 units of the graph of $g\left(x\right)$ .

  

(g)

To determine

To sketch: the graph of $y=g\left(x\right)+1$ .

Explanation of Solution

Given information:

The graph of the function $g$ shown:

  

Calculation:

The following points lie on the graph of $y=g\left(x\right)+1$ .

  $\left(-5,2\right),\left(-1,2\right),\left(0,1\right),\left(3,-2\right)$ and $\left(4,1\right)$ . The above points are plotted below using Maple.

The graph is a horizontal shift to right by 1 units of the graph of $g\left(x\right)$ .

  

(h)

To determine

To sketch: the graph of $y=2g\left(x\right)$ .

Explanation of Solution

Given information:

The graph of the function $g$ shown:

  

Calculation:

The following points lie on the graph of $y=2g\left(x\right)$ .

  $\left(-5,2\right),\left(-1,2\right),\left(0,0\right),\left(3,-6\right)$ and $\left(4,0\right)$ . The above points are plotted below using Maple.

The graph is a horizontal shift to right by 2 units of the graph of $g\left(x\right)$ .