# 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 6E
To determine

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

Expert Solution

The function of the shown graph is y=23(x2)(x2)2 .

### 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 2 units horizontally and stretched 2 units vertically.

Thus, subtract 2 from x and multiply y by 2.

Therefore, the given function is changed as follows.

2f(x2)=3(x2)(x2)2

Thus, the function of the shown graph is y=23(x2)(x2)2 .

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