Problem

The graph of $ y = \sqrt{3x - x^2} $ is given. Us…

01:07

Question

Answered step-by-step

Problem 5 Medium Difficulty

The graph of $ f $ is given. Use it to graph the following functions.

(a) $ y = f (2x) $
(b) $ y = f (\frac{1}{2} x) $
(c) $ y = f (-x) $
(d) $ y = -f (-x) $

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Heather Zimmers

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Top Calculus 3 Educators

Watch More Solved Questions in Chapter 1

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Video Transcript

all right, we have the graph of F and we're going to graph several transformations. Starting with y equals F of two X, So that's going to be a horizontal shrink by a factor of two. So every point is going to have half the X coordinate that it had before. So a point with an ex coordinated zero is still a zero a point with the next coordinative one is now at 1/2 a point with the next coordinated four is now at two, and a point with an X coordinate of six is now at three. Notice that the height did not change it all, just the width. Next in part B, we see we're changing it to y equals F of 1/2 X, and that's going to be a horizontal stretch by a factor of two. So the graph is going to be two times this white, so we can take the points and double their X coordinates. So point with an ex coordinated zero is still zero a point with the next coordinative. One is now a two. A point with an X coordinate of four is now eight and a point with an X coordinate of six is now a 12. So then we can connect those points. Notice that the graph did not change in its height. Didn't get taller or shorter. It just got twice as wide. And this next transformation is a reflection across the Y axis. All the positive X values air going to become negative. And if you have any negative X values, they would become positive. So he have an X value of zero is still zero. The next value of one is now negative one, an X value of four is now negative for and an X value of six is now negative. Six. And if we connect those points, we get our new graph, which looks like a reflection of our old one across the y axis. And for this transformation, we see that X axis reflection that we saw in the last problem. But we also see a Y axis reflection, so we have X axis and y axis reflections together. Those make what we call an origin reflection, and it's going to look like the graph is turned 180 degrees so we can start by doing the X axis reflection and then do the Y axis reflection. So the X axis reflection would take us down here. And then the final graph that were interested in will then have the Y axis reflection. So just concentrate on the green one. Ignore the red one and the green one is the answer.

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem

The graph of $ y = \sqrt{3x - x^2} $ is given. Us…

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 3 Educators

Lily An

Anna Marie Vagnozzi

Heather Zimmers

Samuel Hannah

Calculus 3 Courses

Recommended Videos

Watch More Solved Questions in Chapter 1

Video Transcript

James Stewart

Calculus: Early Transcendentals

Lily An

Anna Marie Vagnozzi

Heather Zimmers

Samuel Hannah

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Lily An

Anna Marie Vagnozzi

Heather Zimmers

Samuel Hannah

James StewartCalculus: Early Transcendentals

Lily An

Anna Marie Vagnozzi

Heather Zimmers

Samuel Hannah

James Stewart

Calculus: Early Transcendentals