Study Skills in Action
Study Skills in Action
Reading Your Textbook Like a Manual
Many students avoid opening their textbooks for the same reason many people avoid opening their
checkbooks—anxiety and frustration. The truth? Not opening your math textbook will cause more
anxiety and frustration! Your textbook is a manual designed to help you master skills and understand
and remember concepts. It contains many features and resources that can help you be successful in
your course.
Graphs and
Chapter 4
176
Functions
o Variables
uations in Tw
Eq
4.2 Graphs of
g method.
point-plottin
ns using the
graphs.
hs of equatio
to sketching
Sketch grap
epts as aids
sketch
x- and y-interc
equation and
an
use
e
and
writ
to
Find
ing method
al problem-solv
Use the verb
its graph.
(1)
o Variables
in Tw
by points
an Equation
be represented
h of
variables can
is called the grap
involving two
all such points
of an equation
em. The set of
The solutions
syst
te
dina
ar coor
on a rectangul
the equation.
The Graph of
ing a Graph
d of Sketch
tting Metho
variables.
The Point-Plo
ting one of the
tion by isola
rewrite the equa
tion points.
1. If possible,
ing several solu
of values show
te system.
2. Make a table
ngular coordina
points on a recta
e
thes
line.
Plot
or
3.
smooth curve
points with a
4. Connect the
(3)
Sketching the
(2)
Sketch the grap
h of 3x + y =
Graph of an
SSmart Study Strategy
Equation
Use the Features of Your Textbook
U
5.
the left.
is isolated on
for y, so that y
ing the equation
tion.
Begin by solv
Write original equa
5
=
y
3x +
each side.
Subtract 3x from
y = −3x + 5
w.
as shown belo
table of values,
3
2
Next, create a
1
0
−1
−4
−2
−1
2
x
5
8
(3, −4)
11
−1)
5
(2,
+
−3x
2)
=
(1,
y
(0, 5)
(−1, 8)
t (−2, 11)
x
plete the
Solution poin
on a line, so com
all six points lie
It appears that
solution points.
the
ts.
plot
poin
,
the
Now
a line through
ing
draw
by
sketch
h.com
SOLUTION
y
12
6
y = −3x + 5
4
2
−8 −6 −4 −2−2
4
8
6
10
−4
−6
(4)
x
11
y
Chapter 4
10
9
tions
1
ary
learn?
Explanation and
y
y-axis 5
4
2
Examples
Review Exercis
es
1−8
Distance x-coordinate
from
y-coordinate
y-axis
(3, 2)
1
−2 −1
−1
Determine wheth
er ordered pairs
are solutions of
equations
( p. 171).
tt 3FBEBOEVOEFSTUBOEUIFDPOUFOUTPGBMM
tinted concept boxes (3)—these contain
important definitions and rules.
7
8
3
Distance
from x-axis
1
2
Origin
3
4
5
x-axis
6
7
x
To verify that an
ordered pair (x,
y) is a solution
with variables
of an equation
x and y, use the
following steps
1. Substitute the
9௘−16
.
values of x and
y into the equat
2. Simplify each
ion.
side of the equat
ion.
3. If each side
simpli¿es to the
same number,
pair is a solution.
then
the ordered
If the two sides
yield different
then the ordered
numbers,
pair is not a soluti
on.
Use the verbal
problem-solving
method to plot
Construct a verba
points on a
l model and assig
rectangular coord
n labels to write
for a real-life probl
inate system
an equation
em. Use the equat
( p. 172).
ion to construct
17, 18
values. Plot the
a table of
ordered pairs repre
sented by the table
of values.
Sketch graphs
of equations using
the point-plotting
1. If possible,
method ( p. 176).
rewrite the equat
ion by isolating
variables.
one of the
2. Make a table
19−30
of values show
ing several soluti
3. Plot these point
on points.
s on a rectangular
coordinate syste
4. Connect the
m.
4.2
points with a smoo
th curve or line.
Find and use xand y-intercept
s as
aids to sketching
To ¿nd the x-inte
graphs ( p. 178).
rcept(s), let y
= 0 and solve
To ¿nd the y-interc
the equation for
ept(s), let x =
x.
Use the verbal
0 and solve the
31−36
problem-solving
equation for y.
method to write
Construct a verba
an equation and
l
model and assig
sketch its graph
for a real-life probl
n labels to write
( p. 180).
an equation
em. Sketch a graph
of the equation.
37, 38
Identify the doma
in and range of
a A relation
relation ( p. 184).
is any set of order
ed pairs. The set
in the ordered
of ¿rst component
pairs is the doma
s
in of the relation.
second component
39−42
The set of
s is the range of
the relation.
Determine wheth
er relations are
functions ( p. 185).
A function is a
relation in which
4.3
no two ordered
same ¿rst comp
pairs have the
onent and differ
ent second comp
Use function notat
43−48
onents.
ion and evaluate
functions ( p. 187).
The function y
= 2x − 6 can
be given the name
in function notat
“f ” and written
ion as f (x) = 2x
− 6.
49−54
Identify the doma
in and range of
a The doma
function ( p. 188).
in of a function
may be explicitly
the function, or
described along
it may be impli
with
ed by the conte
xt.
55−58
978128507469
6 04
Reac
AlgebraWithin
4 Chapter Su
mm
What did you
4.1
at
tutorial videos
Graphs and Func
Plot points on
a rectangular
coordinate syste
m ( p. 168).
(6)
& Spanish and
tt 3FBEUIFMJTUPGTLJMMTZPVTIPVMEMFBSO(1) at
the beginning of this section. If you cannot
remember how to perform a skill, review the
appropriate example (2) in the section.
to
use the results
e the table and
1 and 2, complet
In Exercises
an Equation
of
ph
ers.
Gra
Answ
l
Sketching the
n. See Additiona
h of the equatio
2. y = x − 1
sketch the grap
2
1
0
−1
−2
x
1. y = 9 − x
1
0
−1
2
−2
1
−3
0
y
−1
−22
218
(5)
ish
Solutions in Engl
®
To review what you learned in a previous class:
To prepare for homework:
t $PNQMFUFBGFXPGUIFFYFSDJTFT(4) following
each example. If you have difficulty with any
of these, reread the example or seek help
from a peer or instructor.
To review for quizzes and tests:
t .BLFVTFPGUIF$IBQUFS4VNNBSZ(5). Check
off the concepts (6) you know, and review
those you do not know.
t $PNQMFUFUIF3FWJFX&YFSDJTFT5IFOUBLF
UIF.JE$IBQUFS2VJ[$IBQUFS5FTUPS
Cumulative Test, as appropriate.
193