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Match each equation with its graph. Explain your choices. (Don't use a computer or graphing calculator.)

(a) $ y = x^2 $ (b) $ y = x^5 $ (c) $ y = x^8 $

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01:38

Jeffrey Payo

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 2

Mathematical Models: A Catalog of Essential Functions

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Emerson A.

October 18, 2020

Johns Hopkins University

Missouri State University

Oregon State University

Boston College

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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in this problem. We want to match the equations with the graphs, and so hopefully we're familiar enough with y equals X squared. We've had lots of practice with those that we should look like a parabola with its Vertex at 00 and that graph matches with H. Okay, when we look at y equals X to the fifth power, we realized that that's an odd function, so it should demonstrate, Ah, symmetry about the origin, and that's the one that's going to look like this. And so that goes with Graf F. Obviously, the only one we have left is G. But why does it match with G? When you see something like X to the eighth or X to the sixth or extra the fifth, they're going to behave very similarly to y equals X squared. It's going to be uneven function there just a little bit wider at the bottom, and that matches with graph g

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