Determine the domain and range of the given function:
y = –x4 + 4
This is just a garden-variety polynomial. There are no denominators (so no division-by-zero problems) and no radicals (so no square-root-of-a-negative problems). There are no problems with a polynomial. There are no values that I can't plug in for x. When I have a polynomial, the answer for the domain is always:
the domain is "all x".
The range will vary from polynomial to polynomial, and they probably won't even ask, but when they do, I look at the picture:
graph
The graph goes only as high as y = 4, but it will go as low as I like. Then:
The range is "all y ≤ 4".