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

(a) $ y = 3x $ (b) $ y = 3^x $ (c) $ y = x^3 $ (d) $ y = \sqrt[3]{x} $

a. $[G]$b. $[f]$c. $F$d. $[g]$

01:46

Jeffrey P.

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

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all right, we have some equations and we want to match them with graphs. So let's take a look at a y equals three. X is a linear function. We've had a lot of practice with linear functions ever since. Algebra one, so expecting to see a line. So when you look at the graph options you have, you'll notice that that is capital G. Y equals three to the X. Power is an exponential function. Looks like exponential growth, and I'm sure you've had experience with those two. Exponential growth has that kind of behavior that looks like graph f y equals X. Cubed is another polynomial function, and because it has an odd power, it's going to be an odd function. You're going to see some symmetry about the origin, and when you cube numbers, they grow big rather quickly. So it's going to look like that. So that is actually capital F. And then the cube root function is the inverse of Hugh being function. So it's going to be the reflection of the Cuban function across the line Y equals X. So it looks like this, and that's our graph lower case G

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