Equations of the form *f(x) = g(x)* may be solved
for *x* graphically using the function generation
and plotting capabilities of XYPLOT. The general procedure
is to create the functions *f(x)* and *g(x)* and
to identify the *points of intersection* between the
two curves. Some examples are given below.

In this case *f(x) = x*^{5} + x + 1 and *g(x) = 0*.
Example 1.4 illustrated how to
generate the function *f(x)*. The function *g(x)* need not
be generated since XYPLOT draws the *y = 0* axis line.
- Generate
*f(x)* over the interval (-2,2) using a step size
of 0.01 or finer. *Note:* You have to make a guess about the
region in which the solution is likely to exist; in this case we
chose the *domain* interval to be (-2,2).
- Look at the plot of
*f(x)* and
identify the point at which it crosses through the horizontal axis
line (*y = 0*).
- Zoom in on the region about the point of
intersection, place the cursor on the point and read the
*x*
coordinate from the display.
- Check your solution for
*x* by plugging it into the equation.

*Tip:* Use the *line* plotting symbol to help
*interpolate* the point of intersection.

For this case *f(x) = e*^{-x} and *g(x) = x*.
- Generate
*f(x)* using *Template*
once and the *Rescale*
operation twice. The first *Rescale* expression is `y*-1`,
and the second is `exp(y)`.
- Generate
*g(x)* using *Template*.
- Find the point of intersection between the two curves in
the plot.
- Check your solution for
*x* by plugging it into the equation.