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

1 Answer
Jun 15, 2018

Answer:

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#