Determine if Odd, Even, or Neither f(x)=x^3+x^2-4

$f (x) = x^{3} + x^{2} - 4$

Find $f (- x)$ .

Find $f (- x)$ by substituting $- x$ for all occurrence of $x$ in $f (x)$ .

$f (- x) = {(- x)}^{3} + {(- x)}^{2} - 4$

Simplify each term.

Apply the product rule to $- x$ .

$f (- x) = {(- 1)}^{3} x^{3} + {(- x)}^{2} - 4$

Raise $- 1$ to the power of $3$ .

$f (- x) = - x^{3} + {(- x)}^{2} - 4$

Apply the product rule to $- x$ .

$f (- x) = - x^{3} + {(- 1)}^{2} x^{2} - 4$

Raise $- 1$ to the power of $2$ .

$f (- x) = - x^{3} + 1 x^{2} - 4$

Multiply $x^{2}$ by $1$ .

$f (- x) = - x^{3} + x^{2} - 4$

A function is even if $f (- x) = f (x)$ .

Check if $f (- x) = f (x)$ .

$- x^{3} + x^{2} - 4$ $\neq$ $x^{3} + x^{2} - 4$

Since $- x^{3} + x^{2} - 4$ $\neq$ $x^{3} + x^{2} - 4$ , the function is not even.

The function is not even

A function is odd if $f (- x) = - f (x)$ .

Find $- f (x)$ .

Multiply $x^{3} + x^{2} - 4$ by $- 1$ .

$- f (x) = - (x^{3} + x^{2} - 4)$

Apply the distributive property.

$- f (x) = - x^{3} - x^{2} + 4$

Since $- x^{3} + x^{2} - 4$ $\neq$ $- x^{3} - x^{2} + 4$ , the function is not odd.

The function is not odd

The function is neither odd nor even