What is the domain and range of y =4x - x^2y=4x−x2?

1 Answer
sf
Jun 15, 2018

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

Explanation:

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

To find the range notice you can factor yy as x(4-x)x(4−x). Therefore, the roots are at 0,40,4. By symmetry you know that the maximum will take place in the middle of that, that will say when x=2x=2. The reason its a max value is because of the negative sign on the x^2x2 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

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