Algebra Examples

y = x

$y = x$

Step 1

There are three types of symmetry:

1. X-Axis Symmetry

2. Y-Axis Symmetry

3. Origin Symmetry

Step 2

(x, y)

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

1. X-Axis if

(x, - y)

$(x, - y)$ exists on the graph

2. Y-Axis if

(- x, y)

$(- x, y)$ exists on the graph

3. Origin if

(- x, - y)

$(- x, - y)$ exists on the graph

Step 3

Check if the graph is symmetric about the

x

$x$ -axis by plugging in

- y

$- y$ for

y

$y$ .

- y = x

$- y = x$

Step 4

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

Not symmetric to the x-axis

Step 5

Check if the graph is symmetric about the

y

$y$ -axis by plugging in

- x

$- x$ for

x

$x$ .

y = - x

$y = - x$

Step 6

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

Not symmetric to the y-axis

Step 7

Check if the graph is symmetric about the origin by plugging in

- x

$- x$ for

x

$x$ and

- y

$- y$ for

y

$y$ .

- y = - x

$- y = - x$

Step 8

Multiply both sides by

- 1

$- 1$ .

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Step 8.1

Multiply each term by

- 1

$- 1$ .

- - y = - - x

$- - y = - - x$

Step 8.2

Multiply

- - y

$- - y$ .

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Step 8.2.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

1 y = - - x

$1 y = - - x$

Step 8.2.2

Multiply

y

$y$ by

1

$1$ .

y = - - x

$y = - - x$

y = - - x

$y = - - x$

Step 8.3

Multiply

- - x

$- - x$ .

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Step 8.3.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

y = 1 x

$y = 1 x$

Step 8.3.2

Multiply

x

$x$ by

1

$1$ .

y = x

$y = x$

y = x

$y = x$

y = x

$y = x$

Step 9

Since the equation is identical to the original equation, it is symmetric to the origin.

Symmetric with respect to the origin

Step 10