Question

The function ​f(x)equalsx squared plus 3 x minus 10 models the area of a rectangle.

a. Describe the length and width of the rectangle in terms of x.

b. What is a reasonable domain and range for the​ situation? Explain.

Answer 1

Explanation:

The function ​f(x)equalsx squared plus 3 x minus 10 models the area of a rectangle.

`f(x)=x^2+3x-10`

factor the right side of the expression to find length and width

product is -10

and sum is +3

`5 \cdot -2= -10\\5+(-2)=3`

`f(x)=x^2+3x-10\\f(x)=(x+5)(x-2)`

Area of the rectangle is f(x)

Area = length times width

`f(x)=(x+5)(x-2)\\Area=(x+5)(x-2)`

Length is x+5

width is x-2

the value of x cannot be negative

width is x-2, so x should be greater than 2

Domain is x>2

range is all positive values of y that is area

so range is f(x)>0