# To graph: the function f ( x ) = 3 − 2 ( x − 1 ) 2 using the graph of a standard function and then applying transformations. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.5, Problem 44E
To determine

## To graph: the function f(x)=3−2(x−1)2 using the graph of a standard function and then applying transformations.

Expert Solution

### Explanation of Solution

Given information:

the function is f(x)=32(x1)2

Graph:

To plot the graph of f(x)=x2 ,use the plotting points method, substitute different value of x on f(x)=x2 to determine corresponding value of f(x) .

The table is thus obtained as:

 x -3 -2 -1 1 2 3 y 9 4 1 1 4 9

now plot each point of x along the horizontal axis and the corresponding value of f(x)=y along vertical axis and connect each point to form a smooth curve.

The graph of f(x)=x2 is obtained as: Now, the graph of f(x)=32(x1)2 is the graph of f(x)=x2 shifted 1 unitright, then shrink the graph f(x)=(x1)2 vertically by a factor of 2 , then reflected the graph f(x)=2(x1)2 in the x -axis , then shifted the graph f(x)=2(x1)2 3 unit upwards.

The graphof f(x)=32(x1)2 is obtained as: Interpretation:

From the above graph it can be obtained that the graph of f(x)=32(x1)2 is obtained by shifting the graph of f(x)=x2 1 unitright, then shrinking the graph f(x)=(x1)2 vertically by a factor of 2 , then reflecting the graph f(x)=2(x1)2 in the x -axis , then shifting the graph f(x)=2(x1) 3 unit upwards.

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