a. To evaluatethe function,you can “trace”on the graph.Pressthe button.You shouldsee the
equationat the top of the screen,and the cursorshouldbe on the y-intercept,(0, 1). At the bottomof the
screenyou shouldsee x = 0 and y = 1.Thistells us that forx= 0, the functionvalueis 1.
Now that you are in tracingmode,you can enteranyxvalue,and the calculatorwill tell you theyvalue.For
example,if you press , you will see the cursormoveto the point(2, -3) and at the bottomof the
screen,you will see x = 2 and y = -3. If you press- , you will see x = -2 and y = -19 at the bottom
of the screen.Noticethat you cannotsee the pointon the graph.To see that point,we needto changethe
window. Press and scrolldownto Ymin.Changethe -10 to -25. Thenpress. Now press
-. You shouldsee the point(-2, -19).
b. End behavior:the left-handside of the graphappearsto be goingdown,and the right-handside appears
to be goingup. If we want to see moreof the graph,we can zoomout. Press. This will increase
the size of the window. If you press again,the windowwill increaseagain.If you do this twice,you
will noticethat the axeslook thickand that the graphis hard to see. This is becausethe tick markson the
axesare set in 1’s. Press and scrolldownto Xscl.If you press , this will removeall tick
marks.(You can also set the scaleto somethinglarger.). To see the graphbetter, you can also reducethe
Xminand Xmax.Set Xminto -20 and Xmaxto 20. Press. Nowyou can see the function.Press
in eitherdirection,and you will be able to see that the left-handside of the graphcontinuesgoing
down,and the right-handside continuesgoingup.
c. The x-intercepts:to returnthe graphto a smallerwindow, press. If you wantto see the graphin
a smallerwindow, press. You shouldsee that the graphhas 3 x-intercepts.You can visuallyapprox-
imatethemby tracing:press and movethe cursorleft. The leftmostx-interceptis around-.5. To find
a goodapproximationof the x-intercept,press. This sendsyou backto the graph.On the
screenyou will see the question“Leftbound?”Movethe cursorto the left of the x-intercept.(You will be
movingdown,in this case.)Press. Thenyou will see the question“Rightbound?”Movethe cursor
to the right of the x-intercept,but don’tgo too far (You don’twantto passthe next x-intercept.)Press
. Thenyou will be askedto “guess”the intercept.Movethe cursorbackto the left, as closeto the x-intercept
as possible.Press. You shouldseex= -.5320888.This is an approximationof the x-intercept.If
you use the use samesteps,you will find that the otherx-interceptsare approximately.6527and 2.879.
d. Maximaand minima:noticethat the graphas a “hill” and a “valley.” The hill is calleda “localmaximum”
becauseit is the highestpointon the graph,withina certaininterval.The valleyis similarlya “localminimum.”
To approximatethe coordinatesof the maximum,press and tracecloseto the maximum.It appears
that the maximumis (0, 1). To verifythis, press. To find the maximum,we haveto do the same
“left bound,right bound,guess”processwe usedto find the x-intercepts.This processshouldtell you that
the maximumis(0, 1). (Note:thexvaluemay say somethinglike “9.64487E-7.”This is just a smallcalculator
error. This numberif very closeto 0!) To find the minimum,tracetowardsthe “valley.” (If you want,you can
go to the and makethe Ymina lowernumber, so that you can clearlysee the minimumof the
graph.)Now press. This will bringyou backto the graph.Doingthe “left bound,right bound,
guess”processshouldshowyou that the minimumpointis (2, -3).
Example6:You have100 feet of fencewith whichto enclosea plot of land on the side of a barn.You want
the enclosedland to be a rectangle.
a. Write a functionto modelthe area of the plot as a functionof the widthof the plot.b. Graphthe functionusinga graphingcalculator.c. Whatsize rectangleshouldyou makewith the fencein orderto maximizethe areaof the rectangular
enclosure?
d. Explainthe significanceof the x-intercepts/