Q. 2 Sketch the graph of y=1x.... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 2: Q. 2 (page 100)

Sketch the graph of $y = \frac{1}{x}$ .

Short Answer

Expert verified

The graph of $y = \frac{1}{x}$ is:

Step by step solution

Step 1. Given information

We have been given $y = \frac{1}{x}$ .

We have to sketch it.

Step 2. Find the intercepts.

Put $x = 0$ in $y = \frac{1}{x}$ to find y-intercept.

If we let role="math" localid="1645865267448" $x = 0$ , we obtain a $0$ in the denominator, which is not defined. We conclude that there is no y-intercept.

Put $y = 0$ in $y = \frac{1}{x}$ to find x-intercept.

If we let $y = 0$ , we get the equation $\frac{1}{x} = 0$ which has no solution. We conclude that there is no x-intercept. The graph of $y = \frac{1}{x}$ does not cross or touch the coordinate axes.

Step 3. Find the points satisfying the equation

Find few points satisfying the equation $y = \frac{1}{x}$ .

x	$y = \frac{1}{x}$	(x , y)
localid="1645866731916" $\frac{1}{2}$	2	localid="1645866954649" $(\frac{1}{2}, 2)$
1	1	localid="1645866974829" $(1, 1)$
2	$\frac{1}{2}$	localid="1645866992856" $(2, \frac{1}{2})$
3	localid="1645866805843" $\frac{1}{3}$	localid="1645867005431" $(3, \frac{1}{3})$
$- \frac{1}{2}$	- 2	localid="1645867030742" $(- \frac{1}{2}, - 2)$
$- \frac{1}{3}$	$- 3$	localid="1645867052374" $(- \frac{1}{3}, - 3)$
$- 1$	$- 1$	$(- 1, - 1)$
$- 2$	$- \frac{1}{2}$	$(- 2, - \frac{1}{2})$