Question

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

Answer 1

Step-by-step 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