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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.3, Problem 7E

To determine

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

Expert Solution

The function of the shown graph is

The equation of the given graph is

Let

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 1from*f*(*x*)as it shifted 1 unit downward and then multiply *f*(*x*) by −1 as the graph reflects about *x*-axis.

Therefore, the given function will change as

Thus, the function of the shown graph is