# 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 45E
To determine

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

Expert Solution

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

the range is (,1]

### Explanation of Solution

Given: The function is f(x)=x2+4x3

Calculation:

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

Here, f(x)=x2+4x3 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)=(421)=2

Put the value of x in the function,

f(x)=x2+4x3f(2)=(2)2+4(2)3f(2)=4+83=1

The maximum value of y=1 which occurs at x=2 , Hence the range is (,1] .

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