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Make a rough sketch of the graph of the function.…

01:07

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Problem 11 Easy Difficulty

Make a rough sketch of the graph of the function. Do not use a calculator. Just use the graphs given in Figures 3 and 13 and, if necessary, the transformations of Section 1.3.

$ y = 4^x - 1 $


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02:57

Jeffrey Payo

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 4

Exponential Functions

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Functions

Integration Techniques

Partial Derivatives

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Top Calculus 3 Educators
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04:31

Multivariate Functions - Intro

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

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12:15

Partial Derivatives - Overview

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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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

Okay, So when making a refs catch of a function, we just kind of want to know if we know the basic shape of the function and the basic features. And if you want a rough sketch of Y equals four to the X power minus one, you should start with Y equals four to the X power. That's exponential growth, since the base is greater than one. So it looks roughly like this. Now what happens when we subtract one What we know from our experience with transformations that that should shift the graft down one. And the exponential growth function typically has ah, horizontal Assen towed at a height of zero. So who shift that down? One. It's going to have a horizontal asking towed at a height of negative. One soar graph is going to look something like this. If you want to get a little bit less rough, you could go ahead and plug in a couple numbers and plot a couple of specific points.

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Calculus: Early Transcendentals

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