BuyFind

Precalculus: Mathematics for Calcu...

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

Precalculus: Mathematics for Calcu...

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

Solutions

Chapter 3.1, Problem 46E
To determine

To Find: The domain and range of the function.

Expert Solution

Answer to Problem 46E

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

the range is [4,) .

Explanation of Solution

Given: The function is f(x)=x22x3

Calculation:

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

Here, f(x)=x22x3 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)=(221)=1

Put the value of x in the function,

  f(x)=x22x3f(1)=(1)22(1)3f(1)=123=4

The minimum value of y=4 which occurs at x=1 , Hence the range is [4,) .

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