# The domain and range of the function. ### 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 3.1, Problem 47E
To determine

## To Find: The domain and range of the function.

Expert Solution

the domain is all real numbers, that is (,)

the range is [232,) .

### Explanation of Solution

Given: The function is f(x)=2x2+6x7

Calculation:

A quadratic function f(x)=ax2+bx+c is expressed in standard from as: f(x)=a(xh)2+k

Here, f(x)=2x2+6x7 is a polynomial function, so there is no value that will restrict the domain. Therefore, the domain is all real numbers, that is (,)

As a>0 , there is minimum value is f(b2a)

x=(b2a)=(622)=32

Put the value of x in the function,

f(x)=2x2+6x7f(32)=2(32)2+6(32)7f(32)=232

The minimum value of y=232 which occurs at x=32 , Hence the range is [232,) .

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