# Thread: Odd and Even Functions

1. ## Odd and Even Functions

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?

2. Originally Posted by fabxx
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?

For a function $y(x)$ to be even, then $y(-x) = y(x)$, and for $y(x)$ to be odd, then $y(-x) = -y(x)$.

For a), since $y(-1) = y(1) = 2$ and $y(-4) = y(4) = 7$, 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.

$y(-1) = (-1)^3 - 1 = -1 - 1 = -2$

$y(1) = 1^3 - 1 = 1 - 1 = 0$.

Since $y(-x) \neq -y(x)$, the function can't be odd.

3. But how about for a) (0,4)? The inverse isn't listed. Does this mean that the function is still even?