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If a graph does not change when reflected over a line or rotated around a point,
the graph is symmetric with respect to that line or point. The following
graph is symmetric with respect to the *x*-axis (*y* = 0). Note that if (*x*, *y*) is a point on the graph, then (*x*, - *y*) is also a point on the graph.

Symmetry with Respect to the *x*-axis

If a function is symmetric with respect to the *x*-axis, then *f* (*x*) = - *f* (*x*).

The following graph is symmetric with respect to the *y*-axis (*x* = 0). Note
that if (*x*, *y*) is a point on the graph, then (- *x*, *y*) is also a point on the
graph.

Symmetry with Respect to the *y*-axis

If a function is symmetric with respect to the *y*-axis, then *f* (*x*) = *f* (- *x*).

If a graph can be reflected over a line without altering the graph, then that
line is called the axis of symmetry. In the following graph, *x* = 2 is the
axis of symmetry. Note that if (2 + *x*, *y*) is a point on the graph, then (2 - *x*, *y*) is also a point on the graph.

Axis of Symmetry

If a function has an axis of symmetry *x* = *a*, then *f* (*x*) = *f* (- *x* + 2*a*).

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