Chapter 1.1, Problem 51E

a

To determine

To find: the domain of the function $f\left(x\right)=\frac{3}{x-1}$ , by using the table feature of graphing calculator.

Answer to Problem 51E

  $\left\{x|x\ne 1\right\}$

Explanation of Solution

Given information: The function $f\left(x\right)=\frac{3}{x-1}$

Make a table and put the $f\left(x\right)$ function into Y list and observe the y- values in the table.

An error indicates that an x-value is excluded from the domain.

Calculation:

Make a table listing x and y. Put the value of x in the function and evaluate y as shown below.

x	-5	-4	-3	-2	-1	0	1	2	3	4	5
y	$-\frac{3}{6}$	$-\frac{3}{5}$	$-\frac{3}{4}$	$-\frac{3}{3}$	$-\frac{3}{2}$	$-\frac{3}{1}$	ERROR	$\frac{3}{1}$	$\frac{3}{2}$	$\frac{3}{3}$	$\frac{3}{4}$

The domain for this function includes all real number, except $x\ne 1$ . Hence the domain for $f\left(x\right)$ is $\left\{x|x\ne 1\right\}$

b

To determine

To find: the domain of the function $g\left(x\right)=\frac{3-x}{5+x}$ , by using the table feature of graphing calculator.

Answer to Problem 51E

  $\left\{x|x\ne -5\right\}$

Explanation of Solution

Given information: The function $g\left(x\right)=\frac{3-x}{5+x}$

Make a table and put the $g\left(x\right)$ function into Y list and observe the y- values in the table.

An error indicates that an x-value is excluded from the domain.

Calculation:

Make a table listing x and y. Put the value of x in the function and evaluate y as shown below.

x	-6	-5	-4	-3	-2	-1	0	1	2	3	4
y	$-\frac{9}{1}$	ERROR	$\frac{7}{1}$	$\frac{6}{2}$	$\frac{5}{3}$	$-\frac{3}{1}$	$\frac{3}{5}$	$\frac{2}{6}$	$\frac{1}{7}$	$\frac{0}{8}$	$-\frac{1}{9}$

The domain for this function includes all real number, except $x\ne -5$ . Hence the domain for $g\left(x\right)$ is $\left\{x|x\ne -5\right\}$ .

c.

To determine

To find: the domain of the function $h\left(x\right)=\frac{x^2-12}{x^2-4}$ , by using the table feature of graphing calculator.

Answer to Problem 51E

  $\left\{x|x\ne -2,x\ne 2\right\}$

Explanation of Solution

Given information: The function $h\left(x\right)=\frac{x^2-12}{x^2-4}$

Make a table and put the $h\left(x\right)$ function into Y list and observe the y- values in the table.

An error indicates that an x-value is excluded from the domain.

Calculation:

Make a table listing x and y. Put the value of x in the function and evaluate y as shown below.

x	-5	-4	-3	-2	-1	0	1	2	3	4	5
y	$\frac{13}{21}$	$\frac{4}{12}$	$-\frac{3}{5}$	ERROR	$\frac{11}{3}$	$\frac{12}{4}$	$\frac{11}{3}$	ERROR	$-\frac{3}{5}$	$\frac{3}{3}$	$\frac{13}{21}$

The domain for this function includes all real number, except $x\ne -2\text{ and }x\ne 2$ . Hence the domain for $h\left(x\right)$ is $\left\{x|x\ne -2,x\ne 2\right\}$ .