# 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 48E
To determine

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

Expert Solution

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

the range is (,7] .

### Explanation of Solution

Given: The function is f(x)=3x2+6x+4

Calculation:

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

Here, f(x)=3x2+6x+4 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 maximum value is f(b2a)

x=(b2a)=(62(3))=1

Put the value of x in the function,

f(x)=3x2+6x+4f(1)=3(1)2+6(1)+4f(1)=3+6+4=7

The maximum value of y=7 which occurs at x=1 , Hence the range is (,7] .

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