56 CHAPTER 2 Linear Equations, Inequalities, and Applications
STUDY SKILLS
You are ready to do your homework AFTERyou have read the corresponding textbook
section and worked through the examples and Now Try exercises.
Homework Tips
N Work problems neatly.Use pencil and write legibly, so
others can read your work. Skip lines between steps.
Clearly separate problems from each other.
N Show all your work.It is tempting to take shortcuts.
Include ALL steps.
N Check your work frequently to make sure you are on the
right track.It is hard to unlearn a mistake. For all odd-
numbered problems, answers are given in the back of the
book.
N If you have trouble with a problem, refer to the corre-
sponding worked example in the section.The exercise
directions will often reference specific examples to re-
view. Pay attention to every line of the worked example
to see how to get from step to step.
N If you are having trouble with an even-numbered prob-
lem, work the corresponding odd-numbered problem.
Check your answer in the back of the book, and apply
the same steps to work the even-numbered problem.
N Mark any problems you don’t understand.Ask your
instructor about them.Select several homework tips to try this week.
Tackling Your Homework
(^194) CHAPTER 3Graphs, Linear Equations, and Functions
xy02
–2 2
y = f(x) xy02
2
y = f(x)xy02
2y = f(x)
xy–2 02
–2y = f(x)on the Video Resources on DVDComplete solution available3.6 EXERCISES
1.Concept CheckChoose the correct response:The notation
A.the variable ƒ times 3, or 3ƒ. means
B.the value of the dependent variable when the independent variable is 3.
C.the value of the independent variable when the dependent variable is 3.
D.ƒ equals 3.
2.Concept CheckGive an example of a function from everyday life. (
blanks: depends on , so is a function of .) Hint:Fill in the
Let and. Find the following.
- See Examples 1–3.
- For each function, find 22.
- (a) and (b). See Examples 4 and 5.
ƒ= 51 - 1, 3 2 , 1 4, 7 2 , (^1) 0, 6 2 , 1 2, 2 (^26) ƒ= (^51) 2, 5 2 , 1 3, 9 2 , 1 - 1, 11 (^2) , 1 5, 3 26
ƒ= 51 - 2, 2 2 , 1 - 1, - (^12) , 1 2, - (^126) ƒ= 51 - 1, - 52 , (^1) 0, 5 2 , 1 2, - 526
ƒ (^122) ƒ 1 - 12
ƒ 1 x+h 2 - ƒ 1 x (^2) ƒ (^142) - g (^142) ƒ 1102 - g (^1102)
ƒ 1 x+h 2 ƒ^1 x-^22 g^1 p^2 g 1 e 2
ƒ 1 x+ 22 g^1 k^2 ƒ^1 - x^2 g^1 - x 2
ƒ 1 p 2 g^1 1.5^2
ƒa ƒa^73 b g 1 0.5 2
1
3 b
ƒ 1 - (^32) g 1 - (^22) g (^1102)
ƒ 102 g^1 x^2 =-x^2 +^4 x+^1
ƒ 1 x 2 =- 3 x+ 4
ƒ (^132)
–1 2
(^35)
(^1015)
(^1927)
f
(^25)
–1 3
1
7
20
f
x
24
(^1100)
- 21 41
y=ƒ 1 x (^2) x
5386
20
(^4) - 6
1 - 3
y=ƒ 1 x 2OBJECTIVES Amathematical modelis an equation or inequality that describes a real situation.
Models for many applied problems, called formulas,already exist. A formula is an
equation in which variables are used to describe a relationship. For example, the for-
mula for finding the area of a triangle is
Here,bis the length of the base and his the height.
SeeFIGURE 1. A list of formulas used in algebra is
given inside the covers of this book.
a=
12 bh.
a
Formulas and Percent
2.2
1 Solve a formula for
a specified variable.
2 Solve applied
problems by using
formulas.
3 Solve percent
problems.
4 Solve problems
involving percent
increase or decrease.hb
FIGURE 1