# The function f ( x ) = ( x − 4 ) 2 + 3 in words. ### 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 2.1, Problem 4E

(a)

To determine

## The function f(x)=(x−4)2+3 in words.

Expert Solution

The function f(x)=(x4)2+3 in words is “Subtract 4, then square and add 3.

### Explanation of Solution

The given function is,

f(x)=(x4)2+3 .

The term (x4) is written in words as “Subtract 4”.

The term (x4)2 is written in words as “Subtract 4, then square”.

The term (x4)2+3 is written in words as “Subtract 4, then square and add 3”.

Thus, the function f(x)=(x4)2+3 in words is “Subtract 4, then square and add 3.

(b)

To determine

### The value for f(x) at different values of x in the table.

Expert Solution

The table is filled as given below,

 x f(x) 0 19 2 7 4 3 6 7

### Explanation of Solution

Given:

The given function is,

f(x)=(x4)2+3 (1)

The table of different values is given below,

 x f(x) 0 19 2 4 6

Calculation:

Substitute 2 for x in equation (1), to find the value of f(x) at x=2 ,

f(2)=(24)2+3=(2)2+3=4+3=7

Substitute 4 for x in equation (1), to find the value of f(x) at x=4 ,

f(4)=(44)2+3=(0)2+3=3

Substitute 6 for x in equation (1), to find the value of f(x) at x=6 ,

f(6)=(64)2+3=(2)2+3=4+3=7

Thus, the table is filled as given below,

 x f(x) 0 19 2 7 4 3 6 7

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