What is the domain and range of y =4x - x^2?

1 Answer
Jun 15, 2018

Domain: all x in (-infty, infty), range: y in (-infty,4]

Explanation:

Domain is all x's that the function y is not defined on, and in this case y is defined for all x's.

To find the range notice you can factor y as x(4-x). Therefore, the roots are at 0,4. By symmetry you know that the maximum will take place in the middle of that, that will say when x=2. The reason its a max value is because of the negative sign on the x^2 term, which will make the graph a "sad smiley".

So max(y)=y(2)=4(2)-2^2=4

As the functions greatest value is 4 and it goes to -infty as x->+-infty its range is all y<=4