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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

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 4

Exponential Functions

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Johns Hopkins University

Missouri State University

University of Nottingham

Boston College

Lectures

04:31

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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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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Make a rough sketch of the…

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Make a rough sketch by han…

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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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