CPM Homework Help : CALC Problem 1-82

Are the following functions even, odd, or neither?

$y = x^{1/3}$

$y = -x^2 + 4$

$y = x^3 + x^2 + 1$

Hint (a):

Step 1 (a):

First, check if it is even: $f(a)=a^{\frac{1}{3}}$ $f(-a)=(-a)^{\frac{1}{3}}=-a^{\frac{1}{3}}$
since $f(a) \neq f(-a)$ ,

Step 2(a);

$f(x)$ IS NOT EVEN!
Next, check if it is odd:
$f(-a)=(-a)^{\frac{1}{3}}=-a^{\frac{1}{3}}$
$-f(a)=-a^{\frac{1}{3}}$
since $f(-a)= -f(a)$ ,
$f(x)$ IS ODD!

Hint (b):

Refer to the example in part (a). Be sure to simplify.

Hint (c):

Refer to the example in part (a). Be sure to simplify.