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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

The graph of y = 3 x x 2 is given. Use transformations to create a function whose graph is as shown.

Chapter 1.3, Problem 7E, The graph of y=3xx2 is given. Use transformations to create a function whose graph is as shown. , example  1

Chapter 1.3, Problem 7E, The graph of y=3xx2 is given. Use transformations to create a function whose graph is as shown. , example  2

To determine

To create: A function from the given graph by using transformations.

Explanation

The equation of the given graph is y=3xx2 .

Let y=f(x) .

Notice that the given graph is a semi-circle with the domain [0, 3] and the range [0, 1.5].

Also, it is observed from the given graph that the graph is shifted 4 units to the left and shifted 1 unit downward.

Moreover, the graph is reflected about the origin.

Thus, add 4 to x as it shifted 4 units to the left; subtract 1fromf(x)as it shifted 1 unit downward and then multiply f(x) by −1 as the graph reflects about x-axis

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