Step-by-step explanation:
The function f(x)equalsx squared plus 3 x minus 10 models the area of a rectangle.
[tex]f(x)=x^2+3x-10[/tex]
factor the right side of the expression to find length and width
product is -10
and sum is +3
[tex]5 \cdot -2= -10\\5+(-2)=3[/tex]
[tex]f(x)=x^2+3x-10\\f(x)=(x+5)(x-2)[/tex]
Area of the rectangle is f(x)
Area = length times width
[tex]f(x)=(x+5)(x-2)\\Area=(x+5)(x-2)[/tex]
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
