TI-83, TI-83 Plus, TI-84 Plus Guide
1. Enter the function in some location of the graphing list – say
Y1 = 3.5(1.095^X) and draw a graph of the function. Press
TRACE and hold down either ► or ◄ until you have an
estimate of where the output is 20. Use this
X-value, 19 or
19.4 or 19.36, as your guess in the
SOLVER.
Remember that you can use any letter to represent the input in the solver, but to graph a
function, you must use
X as the input variable.
2. Enter the left- and right-hand sides of the equation in two
different locations of the
Y= list – say Y1 = 3.5(1.095^X) and
Y2 = 20. With the graph on the screen, press TRACE and
hold down either
► or ◄ until you get an estimate of the
X-value where the curve crosses the horizontal line
representing 20.
3. Use the AUTO setting in the TABLE, and with ▲ or ▼
scroll through the table until a value near the estimated out-
put is found. Use this
X-value or a number near it as your
guess in the
SOLVER.
GRAPHICALLY FINDING INTERCEPTS Finding the input value at which the graph of
a function crosses the vertical and/or horizontal axis can be found graphically or by using the
SOLVER. Remember the process by which we find intercepts:
• To find the y-intercept of a function y = f(x), set x = 0 and solve the resulting equation.
• To find the x-intercept of a function y = f(x), set y = 0 and solve the resulting equation.
An intercept is the where the graph crosses or touches an axis. Also remember that the x-
intercept of the function y = f(x) has the same value as the root or solution of the equation
f(x) = 0. Thus, finding the x-intercept of the graph of f(x) – c = 0 is the same as solving
the equation f(x) = c.
We illustrate this method with a problem similar to the one in Activity 32 in Section 1.1 of
Calculus Concepts. Suppose we are asked to find the input value of f(x) = 3x – 0.8x
2
+ 4 that
corresponds to the output f(x) = 2.3. That is, we are asked to find x such that 3x – 0.8x
2
+ 4 =
2.3. Because this function is not given in a context, we have no indication of an interval of
input values to use when drawing the graph. We will use the
ZOOM features to set an initial
view and then manually set the
WINDOW until we see a graph that shows the important points
of the func-tion (in this case, the intercept or intercepts.) You can solve this equation
graphically using either the x-intercept method or the intersection method. We present both,
and you should use the one you prefer.
X
-INTERCEPT METHOD for solving the equation f(x) – c = 0:
Copyright © Houghton Mifflin Company. All rights reserved.
11
To Next Page
Loading...
Need help?
General
