Determine if Odd, Even, or Neither 2x-1

$2 x - 1$

Write $2 x - 1$ as a function.

$f (x) = 2 x - 1$

Find $f (- x)$ .

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

$f (- x) = 2 (- x) - 1$

Multiply $- 1$ by $2$ .

$f (- x) = - 2 x - 1$

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

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

$- 2 x - 1$ $\neq$ $2 x - 1$

Since $- 2 x - 1$ $\neq$ $2 x - 1$ , the function is not even.

The function is not even

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

Find $- f (x)$ .

Multiply $2 x - 1$ by $- 1$ .

$- f (x) = - (2 x - 1)$

Apply the distributive property.

$- f (x) = - (2 x) + 1$

Multiply.

Multiply $2$ by $- 1$ .

$- f (x) = - 2 x + 1$

Multiply $- 1$ by $- 1$ .

$- f (x) = - 2 x + 1$

Since $- 2 x - 1$ $\neq$ $- 2 x + 1$ , the function is not odd.

The function is not odd

The function is neither odd nor even