Question

describe the similarities and differences between y=x^2 and a power function with a even degree higher than two?

please help me!!!

i wrote that the domain and range were the same for even funnctions. i wrote that they both share the vetical relfection charcetsitc, and the end behavior. by the way my teaher doesnt like saying from quadrant 1 to 2 for end behaviour is there another way of saying it? theay both have similar shapes.

differnces
i wrote that there is none. i toke the exaple y=x^2 and y= x^4. i didntsee anyother differenceexcept that y= x^4 seemed to be streched. is there more i can write for differences?

Answer 1

Similarities: Domain and Range the same. Same end behavior, you could say "as x approaches infinity or negative infinity".
Differences: They don't have the same reflection characteristics because an x^4 function can have non-symmetrical bumps in it. They're not always parabola shaped.
An x^2 function has 2 zeros, an x^4 has 4, and so on.
An x^2 function can be solved by using the quadratic formula, others cannot.