# To create: A function from the given graph by using transformations. ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

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 y=3(x+4)(x+4)21 .

### Explanation of Solution

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.

Therefore, the given function will change as y=f(x+4)1 .

Thus, the function of the shown graph is y=3(x+4)(x+4)21 .

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