Section 2.2
The Graph of a Function
109
Version: Fall 2007
2.2
Exercises
Perform each of the following tasks for
the functions defined by the equations in
Exercises 1

8
.
i.
Set up a table of points that satisfy
the given equation. Please place this
table of points next to your graph on
your graph paper.
ii.
Set up a coordinate system on a sheet
of graph paper. Label and scale each
axis, then plot each of the points from
your table on your coordinate system.
iii. If you are confident that you “see”
the shape of the graph, make a “leap
of faith” and plot
all
pairs that sat
isfy the given equation by drawing
a smooth curve (freehand) on your
coordinate system that contains all
previously plotted points (use a ruler
only if the graph of the equation is
a line). If you are not confident that
you “see” the shape of the graph, then
add more points to your table, plot
them on your coordinate system, and
see if this helps. Continue this process
until you “see” the shape of the graph
and can fill in the rest of the points
that satisfy the equation by drawing
a smooth curve (or line) on your co
ordinate system.
1.
f
(
x
) = 2
x
+ 1
2.
f
(
x
) = 1
−
x
3.
f
(
x
) = 3
−
1
2
x
4.
f
(
x
) =
−
1 +
1
2
x
5.
f
(
x
) =
x
2
−
2
6.
f
(
x
) = 4
−
x
2
Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/
1
7.
f
(
x
) =
1
2
x
2
−
6
8.
f
(
x
) = 8
−
1
2
x
2
Perform each of the following tasks for
the functions
Exercises 9

10
.
i.
Set up a coordinate system on a sheet
of graph paper. Label and scale each
axis.
ii.
Use the table feature of your graph
ing calculator to evaluate the func
tion at the given values of
x
. Record
these results in a table next to your
coordinate system on your graph pa
per.
iii. Plot the points in the table on your
coordinate system then use them to
draw the graph of the given function.
Label the graph with its equation.
9.
f
(
x
) =
√
x
−
4
at
x
= 4
, 5, 6, 7, 8,
9, and 10.
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 ObjectOriented Programming, The Table, Coordinate system, Graph of a function

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