Question

Which function is an odd function? f(x)=0.8x^3, f(x)=5x^2, f(x)=0.7x^2 + 3, or f(x)=3x - 1.

Answer 1

A function is odd if f(-x) = -f(x) in other words, if you negative the input, the output is negatived as well. For the first one:

f(x)=0.8x^3 and f(-x)=0.8(-x)^3 which simplifies to -0.8*x^3

so that's the answer (assuming there's only one-- the others turn out to be a parabola and a straight line, and lines can only be odd if they pass through 0,0 (which this one doesn't).

Answer 2

hint: An odd function satisfies f(-x)=-f(x).
For example, f(x)=-x is odd, because f(-x)=-(-x)=-f(x) for all values of x.