Hey this is on the Barron's SAT Math IIC Book page 45
Which of the following functions is neither odd nor even?
a) {(1,2),(4,7), (-1,2), (0,4), (-4,7)}
c) {(x,y):y=x^3-1}
why is a) even or odd?
and isn't c) odd?
Thanks in advance
For a function $\displaystyle y(x)$ to be even, then $\displaystyle y(-x) = y(x)$, and for $\displaystyle y(x)$ to be odd, then $\displaystyle y(-x) = -y(x)$.
For a), since $\displaystyle y(-1) = y(1) = 2$ and $\displaystyle y(-4) = y(4) = 7$, the function is even.
For c), all you need is a counter-example.
Pick two x values of the same magnitude, say -1 and 1.
$\displaystyle y(-1) = (-1)^3 - 1 = -1 - 1 = -2$
$\displaystyle y(1) = 1^3 - 1 = 1 - 1 = 0$.
Since $\displaystyle y(-x) \neq -y(x)$, the function can't be odd.