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Use the given graphs of $ f $ and $ g $ to estimate the value of $ f (g(x)) $ for $ x = -5, -4, -3, . . . , 5 $. Use these estimates to sketch a rough graph of $ f \circ g $.

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05:14

Jeffrey P.

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 3

New Functions from Old Functions

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Missouri State University

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all right, we're going to use these two graphs and we're going to find f of G of X for these 11 different X values, and then we'll use those points, plot them and sketch a rough graph of F of G. So I'm going to go through and find all the G of X values first. So and these air just my sketches or rough sketches and these values might not be exact. So first of all, we have g of negative five that looks like it's at about zero. Do you have negative fours at about one G of negative three is at about two G of negative two is out about 2.5 G of negative one is that about three and G of zero is at about 2.7. We'll say give or take a little Moving to the positive side. G of one is at about three G of two is at about 1.5. Actually, G one is at about two. Let's go back and change that. Do you have to? Is at about 1.5 G of three is at about zero. JIA, four is at about negative 1.5. Actually, if you look at the actual the rial graph in the book, it's at about negative, too. And G of five is at about negative for okay, so now we'll find the F values. So what we're going to do is find f of the value we just found. So for the 1st 1 it's f of zero for the next one. It's f of one and so on. So f of zero is about negative for F of one is about negative 3.5 f of to is about negative, too. F of 2.5 is about negative 1.5 F of three is about zero F of 2.7 is about negative 0.5 f of two again negative, too F of 1.5 about negative 2.5 f of zero is negative for F of negative, too, is about negative, too, and F of negative four is about 1.5. So now what we want to do is plot these points and see what the graph of F of G would look like. So I'm going to plot these points in green, so we have the point. Negative five. Negative four Negative for negative. 3.5 Negative three Negative. Too negative to negative 1.5 Negative 10 No. Zero Negative, 1/2 one negative, too, to negative 2.5. Three. Negative four four Negative, too. And 5 1.5 Let's assume that we're just going to connect these with a nice, smooth curve somewhat, and that would be F of G.

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