Algebra Examples

$y = 2^{x}$

There are three types of symmetry:

1. X-Axis Symmetry

2. Y-Axis Symmetry

3. Origin Symmetry

If $(x, y)$ exists on the graph, then the graph is symmetric about the:

1. X-Axis if $(x, - y)$ exists on the graph

2. Y-Axis if $(- x, y)$ exists on the graph

3. Origin if $(- x, - y)$ exists on the graph

Check if the graph is symmetric about the x-axis by plugging in $- y$ for $y$ .

$- y = 2^{x}$

Simplify the left side.

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Remove parentheses.

$- y = 2^{x}$

Since the equation is not identical to the original equation, it is not symmetric to the x-axis.

Not symmetric to the x-axis

Check if the graph is symmetric about the y-axis by plugging in $- x$ for $x$ .

$y = 2^{- x}$

Since the equation is not identical to the original equation, it is not symmetric to the y-axis.

Not symmetric to the y-axis

Check if the graph is symmetric about the origin by plugging in $- x$ for $x$ and $- y$ for $y$ .

$- y = 2^{- x}$

Solve for $y$ .

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Simplify the left side.

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Remove parentheses.

$- y = 2^{- x}$

Simplify the left side.

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Multiply $- (- y)$ .

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Multiply $- 1$ by $- 1$ .

$1 y = - (2^{- x})$

Multiply $y$ by $1$ .

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

Simplify the right side.

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

$y = - 2^{- x}$

Since the equation is not identical to the original equation, it is not symmetric to the origin.

Not symmetric to the origin

Determine the symmetry.

Not symmetric to the x-axis

Not symmetric to the y-axis

Not symmetric to the origin