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" $(- \frac{1}{3}, - 3)$
$- 1$	$- 1$	$(- 1, - 1)$
$- 2$	$- \frac{1}{2}$	$(- 2, - \frac{1}{2})$

Step 4. Sketch the graph

We get the following graph using the points:

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the intercepts.

Step 3. Find the points satisfying the equation

Step 4. Sketch the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Pure Maths

Mechanics Maths

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

Sketch the graph of y=1x.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the intercepts.

Step 3. Find the points satisfying the equation

Step 4. Sketch the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Pure Maths

Mechanics Maths

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

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