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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 = (0.5)^{x - 1} $

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02:13

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

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

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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…

when making a rough sketch of a function. We want to be able to show that we understand the basic shape of the function and its basic features, and we're going to start with the standard function. Why equals 0.5 to the X? That would be exponential decay. Because the base is less than one, it's between zero and one, so roughly that would have this shape. Now we need to show that we understand the transformation of subtracting one from X for any function. When you subtract one from X, you're actually moving the graph to the right one. So we're going to take the graph. We just drew and move it to the right one. Now, the graph we just drew has a horizontal Assen towed at a height of zero. If you move your graph to the right one, you're still going to have a horizontal Assam towed at a height of zero. And the graph we just drew went through the 0.1 That's the Y intercept for basic exponential growth or decay function. So our new graph will go through the 0.11 moving it to the right one. So there's a rough sketch

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