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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 $

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01:01

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

Harvey Mudd College

Baylor 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.

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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$7-10$ Graph the given fun…

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Graph the given functions …

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$3-6$ Graph the given func…

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Use Formula 10 to graph th…

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.

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