Algebra Examples

$f (x) = 2^{x}$

Determine if the function is odd, even, or neither in order to find the symmetry.

1. If odd, the function is symmetric about the origin.

2. If even, the function is symmetric about the y-axis.

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

$f (- x) = 2^{- x}$

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

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

$2^{x} = 2^{x}$

Since $2^{x} = 2^{x}$ , the function is even.

The function is even

Since the function is not odd, it is not symmetric about the origin.

No origin symmetry

Since the function is even, it is symmetric about the y-axis.

Y-axis symmetry