Given an equation of the form
for
use a graphing calculator to approximate the solution.
Press
[Y=] . Enter the given exponential equation in the line headed “
Y
1 = ”.
Enter the given value for
in the line headed “
Y
2 = ”.
Press
[WINDOW] . Adjust the
y -axis so that it includes the value entered for “
Y
2 = ”.
Press
[GRAPH] to observe the graph of the exponential function along with the line for the specified value of
To find the value of
we compute the point of intersection. Press
[2ND] then
[CALC] . Select “intersect” and press
[ENTER] three times. The point of intersection gives the value of
x for the indicated value of the function.
Approximating the solution of an exponential equation
Solve
graphically. Round to the nearest thousandth.
Press
[Y=] and enter
next to
Y
1 =. Then enter 42 next to
Y2= . For a window, use the values –3 to 3 for
and –5 to 55 for
Press
[GRAPH] . The graphs should intersect somewhere near
For a better approximation, press
[2ND] then
[CALC] . Select
[5: intersect] and press
[ENTER] three times. The
x -coordinate of the point of intersection is displayed as 2.1661943. (Your answer may be different if you use a different window or use a different value for
Guess? ) To the nearest thousandth,
While horizontal and vertical shifts involve adding constants to the input or to the function itself, a
stretch or
compression occurs when we multiply the parent function
by a constant
For example, if we begin by graphing the parent function
we can then graph the stretch, using
to get
as shown on the left in
[link] , and the compression, using
to get
as shown on the right in
[link] .
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