Name:

Date:

Total Points Scored:

Points for Full Credit:

1Jmt> + Qbfv'~

1750

Chapter 3 Test Answer the following questions to the best of your ability, making sure to show your work wherever necessary, Please note that some problems are worth more than others,

Problems 1-8: Domain, Range, and Functions (75 points each). State the domain and range of each of the following relations, then state whether or not it is a function,

1) {(- I, 3), (3, - I), (4, 2), (1, O)}

D: t- \ I \, ';, ~ ~ (2.: ~-\ 0 :I ';)

, I •

Yt')

2) {(5, 4), (4, 2), (5, 1), (5, 3)}

0 ', ~ <i, 5 ~ C1-' t \ I~ '7,43

~D

3) x y

4 - 3 3 - 1 2 3 6 - 3

4)

- 6 -5

\:y \L "

-~ - 3 - 1 - I

y.Q~

} '

6

~

~

3

~

1

0 1 1 3 ~ - I

- 1

-3

-.I

-5

-

5) {(- 3, 2), (3, - 1), (3,4), (0, 5)}

D,,\~\c),~1

~ " ~ _ 1 , 1, t!1 r ~ No

5

6) {CO, 4), (3, 0), (1, - 1), (- 3, - 2)}

i)', L -) 0 \ ) ') 1 , I I

a,,\-,,~:2/b,c..15

'f,s

6 \"

\' 8) 6 x y 5 - 4 2

- I 5 4

3

2 0 6 1 2 8

- 6 - 5 -4 - 3 - 2 - I 0 2 3 .j 5 6 \ '

- I

- 2

- 3

-4

-5

-7)

Problems 9-16: Evaluate Functions (25 points each). Find the value of each of the following if [(x) = 3x + 1, g(x) = x 2 - 2x, and hex) = -5 + x .

9) [(3) = ?,.?> +-\ ... to 13) [(2) + h(7) = 3·'hl "'" ~'5"~1

7 4 ~ -- ciJ 10) g(4) = ~~-d·L{-· 10-cr~ riJ 14) g(0)·[(118) = , -:;:l

o·~ ~ t9J

II) h(-2) = -'5 t -~":.G IS) h(c) = &9 12) [(2b) = 3.?-br l .. g 16) [(b) + [(3b) =

3-bl-l j. ~·~'ot-I

7 b+-I ~ 0,&4-/ -. ~)9

Problems 17-20: Arithmetic Sequences (50 points each). Find the next three terms in each of the following sequences, and describe the nth term algebraically. Remember, the nth term of any sequence can be described by the equation:

an = a 1 + (n - l)d

where an is the nth term of the sequence, a 1 is the first term, and d is the common difference. For example, to find the 81h term of the sequence 2,5,8, ... (common difference of +3), your values would be n = 8, a1 = 2, and d = 3, and you would use the following equation:

as = 2 + (8 - 1)3

'}? d ~ ?CI ~. 14 17· ~ I '7 17) 11,14,17, 20, ... " 19) 10,11.5,13,14.5, ... I I

a" ~ It+ 1...,,-\')'3 ~(\ ~ IDt LIl")' \ . ~

7~ ,0 <..0'-( 18) 100, 94, 88, 82, ... I I 20)

3 9 15 21

q (\ : lO"c:) ~ (. (l-l ') . (- & )

Problems 21-24: Graphing (200 points each). For each of the following equations, identify the x- and y-intercepts (if they exist), graph, and say if it is a linear function:

21) 3x + 2y = 8

~_\,,~ '. ("n/3, 0'> (. u 't)

I

y

~ 6

-{ J \ 2

\ 1

I\, - 6 - $ --' - 3 - :! - 1 0 I 2

.•. • ~ 6 - I

-2 \ - .1

... -s

\ . ~

22) Y = -~x + 3 2

x'\" ~ '. (G, D '> ,

~_ " I\+ ~ (()/~'J

23) 2x + y = 3

x.-~I\~ " (~h 0) I

1- ~ ilL l 6 ,?J ')

24) Y = ~X 4

')(. -~ "t " ~-.-,,\ :

l'

~ I" "-

.+ S

!'<; ~

L , ...... 2 ,

- 6 - 5 .... - 3 - :! -, 0 -, -2

-3

-.I

-s _h

" h. II'i 6

I\ S

,1\ ~ \

- 6 - 5 - -I - 3 - 1 - I 0 -, -2

- 3

- -.I

-S _ F.

" 1 rf s

r-~

r- 3

2

14 ' \7 - b - S -.s - 3 -1 - I )

I- 1 -y-' 11 -2

- 3

17 -.I

1/ -s

I ,

...... , 2 3 ~ S ,:-;; "

t-

t-

, , 3 ~ S 6 ." l\.

1\

~

l '[7 1/

I

, 2 3 ~ S (, ..

1

Bonus (10 points each).

25) Is the function y = 3x - 2 a proportional linear function? Why or why not?

26) Does the equation x + 2xy = 7 represent a linear function? Why or why not?

27) Is the equation x = 3 a standard form linear equation? Why or why not?

,

28) Does the quation x = 3 represent a linear function? Why or why not?

~

29) Is the equation -2x + 3y = 9 a standard form linear equation? Why or why not?

30) Is the equation 2x + 4y = 12 a standard form linear equation? Why or why not?

11 I) <-{ ~ \) $w. Co/N"U>" Wt, ( ,-0 I I I

31) A function produces the following table of values. What is the equation of the function (in function notation!)?

+\0