Problem

Graph the given functions on a common screen. How…

01:08

Question

Answered step-by-step

Problem 9 Medium Difficulty

Graph the given functions on a common screen. How are these graphs related?

$ y = 3^x $ , $ y = 10^x $ , $ y = (\frac{1}{3})^x $ , $ y = (\frac{1}{10})^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

Harvey Mudd College

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

Video Transcript

in this problem. We're using a graphing calculator to compare some graphs. We want to see what they have in common and how they were, how they are related. So we go to the y equals menu and we type the four equations in their Michael's three to the X 10 to the X 1/3 to the X and 1/10 to the X for a window. I've chosen to use negative 10 to 10 on my X axis and negative 2 to 20 on my Y axis. And those numbers can be different. Just fiddle around with until you find something you like. Okay, here are all four graphs together. So the blue one is y equals three to the X, and the black one is y equals 1/3 to the X, so noticed that the blue one and the black one are reflections Across the Y axis. The red one is y equals 10 to the X, and the pink one is y equals 1/10 to the X, so noticed that the red one and the pink one are also reflections across the y axis. So if you have the reciprocal of your base, you're going to get a reflection. The two functions that had a base greater than 13 to the X and tend to the X. Those were the exponential growth graphs, and the two that had a base between zero and one, 1/3 and 1/10. Those were the exponential decay graphs. One other thing we can note is that when you have a greater base such as Y equals tend to the X, it's going to be a steeper curve compared with when you have a smaller base, such as Michael's three to the X.

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