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

$ y = e^x $ , $ y = e^{-x} $ , $ y = 8^x $ , $ y = 8^{-x} $

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01:02

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

Missouri State University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

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.

12:15

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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in this problem, we're going to compare some graphs using a graphing calculator. So we go to the y equals menu. We type in the four functions Michael's either the X Y equals E to the opposite of X Michael's A to the X and Y equals eight to the opposite of X. Now, before I look at all four of those graphs at the same time, I'm just going to look at the 1st 2 y equals e to the X and e to the opposite of X. So I've turned off the equal signs on the last two and here we go. Okay, so the blue one is y equals e to the X. That looks like your typical exponential growth. And the red one is y equals each of the opposite of X. These air reflections across the Y axis. Now let's take a look at the other two. So let's turn off the 1st 2 and turn on the last two. Okay, so the black one is y equals eight to the X, and the pink one is y equals eight to the opposite of X notice that these air also reflections across the Y axis So if you replace X with the opposite of X, you reflect across the Y axis. Now let's take a look at y equals E to the X, and why equals eight b x. These are both exponential growth. The one with the base of eight is steeper. And now let's take a look at why equals either the opposite of X and eight Michael's eight to the opposite of X. So these are both exponential decay. The one with the base of eight is deeper, so we had to exponential growth to exponential decay. To that were reflections across the Y axis from one another two pairs.

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