Question
If h(x)=x^3, what is the difference between h(x) reflected about the x-axis and h(x) reflected about the y-axis?
Answers
Steve
x-axis: (x,y)->(x,-y)
y-axis: (x,y)->(-x,y)
but, since h(x) is an odd function
h(-x) = -h(x)
reflecting h(x) through either axis flips it to the same thing.
(x,x^3)->(x,-x^3)
(x,x^3)->(-x,x^3) = (-x,-(-x)^3)
y-axis: (x,y)->(-x,y)
but, since h(x) is an odd function
h(-x) = -h(x)
reflecting h(x) through either axis flips it to the same thing.
(x,x^3)->(x,-x^3)
(x,x^3)->(-x,x^3) = (-x,-(-x)^3)