Chapter 2.2, Problem 46E

To determine

Find the minimum or maximum value of the function .Describe the domain and range of the function, and where the function increasing and decreasing.

Answer to Problem 46E

Minimum value is -4.

Domain is set of all real numbers and range $y\ge -4$ .

The function is decreasing to the left of $x=2$ and increasing to the right of $x=2$ .

Explanation of Solution

Given information:The given function is $y=x^2-4x.$

Calculation:

  $y=x^2-4x.$

Identify the coefficients.

  $a=1,b=-4,c=0.$

Since $a>0$ ,parabola opens up and function has a minimum value.

To find minimum value, calculate coordinates of the vertex.

  $\begin{array}{l}x=-b/2a=-(-4)/2\times 1=4/2=2.\\ f(2)=2^2-4\times 2=4-8=-4.\end{array}$

Minimum value is -4.

Domain is set of all real numbers and range $y\ge -4$ .

The function is decreasing to the left of $x=2$ and increasing to the right of $x=2$ .