Solution:The plot of land will look like the picturebelow:
a. The equation:The areaof the rectangularplot is the productof its lengthand width.We can writethe
area as a functionofx:A(x) = 2xh. We can eliminatehfrom the equationif we considerthat we have 100
feet of fence,and we writean equationabouthow we are usingthat 100 feet of fence:x+ 2h= 100. (The
fourthside of the rectangledoesnot requirefencebecauseof the barn.)We can solvethis equationforh
and substituteinto the area equation:
b. The graph:Press and clearany equations.Thenenterthe equationin Y1. Noticethat if you press
, you will not see any graph.You can zoomout by pressing , but it may be moreefficienttochoosea windowbasedon functionvalues.Press in orderto set up the table.TblStartis the
first entryyou wantto see in the table. Tblallowsyou to set the increments.For example,if you wantto
seex= 1, 2, 3, 4, etc, set this to 1. For this example,set this to 10. Makesure Indpntand Depend(x and
y) are set to “auto.”Thenpress to see the table.If you scrollthroughthe table,you will see that
the y valuereaches 2500 atx= 50, and then the valuesdecrease.Nowwe can set the window. Press
. and set Xmin= -1, Xmax= 105, Ymin= -200,and Ymax= 3000.(Note:you can set Xminand
Ymineachto 0, but settingthemat -1 and -200 allowsyou to see the axes.)
The graphof A(x) is shownhere on the interval[0, 100].