We can also reflect the graph of a function over the *x*-axis (*y* = 0), the
*y*-axis(*x* = 0), or the line *y* = *x*.

Making the output negative reflects the graph over the *x*-axis, or the line *y* = 0. Here are the graphs of *y* = *f* (*x*) and *y* = - *f* (*x*). Note that if (*x*, *y*_{1}) is a point on the graph of *f* (*x*) and (*x*, *y*_{2}) is a point on the graph
of - *f* (*x*), then *y*_{2} = - *y*_{1}. The range also becomes negative; if range =
*f* (*x*):*a* < *f* (*x*) < *b*, then the new range is *g*(*x*):-*b* < *g*(*x*) < -*a*.

Graphs of *f* (*x*) and - *f* (*x*)

Making the input negative reflects the graph over the *y*-axis, or the line *x* = 0. Here are the graphs of *y* = *f* (*x*) and *y* = *f* (- *x*). Note that if (*x*_{1}, *y*)
is a point on the graph of *f* (*x*) and (*x*_{2}, *y*) is a point on the graph of *f* (- *x*), then *x*_{2} = - *x*_{1}. The domain also becomes negative; if domain = *x*:*a* < *x* < *b*, then the new domain is *x*:-*b* < *x* < -*a*.

Graphs of *f* (*x*) and *f* (- *x*)

Switching *x* and *y* reflects the graph over the line *y* = *x* (this is
equivalent to finding the inverse). Now, *x* is a function of *y*.
Here are the graphs of *y* = *f* (*x*) and *x* = *f* (*y*). Note that if (*x*_{1}, *y*_{1}) is
a point on the graph of *f* (*x*) and (*x*_{2}, *y*_{2}) is a point on the graph of
*f* (*y*), then *y*_{1} = *x*_{2} and *y*_{2} = *x*_{1}.

Graphs of *y* = *f* (*x*) and *x* = *f* (*y*)

In addition, we can rotate the graph of a function 180^{o} around the
origin. Making the input and the output of a function negative results in a
rotation of the function around the origin. Here is a graph of *y* = *f* (*x*) and
*y* = - *f* (- *x*). Note that if (*x*, *y*) is a point on the graph of *f* (*x*), then (- *x*, - *y*) is a point on the graph of - *f* (- *x*). The domain and range both become
negative.

Graphs of *f* (*x*) and - *f* (- *x*)

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