Unit Test Study Guide Name: --------------- (Relations and ...
[Pages:8]Unit ! Test Study Guide
(Relations and Functions)
Name: ---------------
Date: ---------- Per: ----
Topic 1: Relations &. Functions
Directions: Identify the domain and range of each of relation. Then, determine whether the
relation is a function.
l.
2.
3.
X
y
-4 8
{(-6, 4), (5, -1 ), (O, 3), (-2, 4)}
-3 l
o -5
-3 2
Domain: Range: Function?
4.
'
Domain:
Range:
Function?
5.
X
y
o
~ 2
4- ..-e---->- 3
-- 9 - 4 5
Domain:
Range:
Function?
6.
X
y
-4 -1 ---- -3
o
, 8
7
Domain:
Range:
Function?
7.
I
\ ,
~
I
'
I I'
I
I
I
I
'
~
.
Domain:
Range:
Function?
Domain:
Range:
Function? 8.
.,,
V V
/
,,
/
/
' V
,,
Domain: Range: Function? 9.
'
Domain: Range: Function?
Domain: Range: Function?
' /
I
\
,,
\
J
' /
Topic 2.: Real World Graphs
Directions: Choose the graph that best represents each situation.
1 O. Corinna is riding a horse on a carousel.
Which graph best represents her
distance from the center of the ride in a single rotation?
-le!
uGI
_Eg
GI
u e
.E ?"'
GRAPH A
11. A cup of hot coffee cools down until it reaches room temperature. Which graph best represents the temperature of the coffee?
GI
:5 ?;?;
0.
E
..G..I
Time
GRAPH A
GRAPH B
;?; ? uGI
_Eg
GI
u e
~ ?
Time
GRAPH B
GI
:5 ?;?;
0.
E
..G..I
12. Mitch went for a hike. He got halfway
up the mountain and realized he had
dropped his compass. He turned
around and walked back. He found
the compass at the point he had
GI
started the hike. He picked it up, then eu
hiked to the top of the mountain.
.E ?"'
Which graph best represents the total
distance he hiked?
Time
GRAPH A
Time
Topic 3: Equations as Functions/Graphing Functions using Tables
Directions: Complete the table, then graph the function.
13. y= -2x+ 5
'~
14.
y
3
=-x-1
2
Time
GRAPH B
GI
e u
.E ?"'
Time
X
y
o
l
3
5
X
y
-
-2
,
o
2
4 ,v
- ,
,
15. Find the range of the function y=~ x + 17 4
when the domain is {-12, -4, 8}.
16. Find the range of the function y= -x2 - 3x when the domain is {-5, O, 2}.
Topic 4: Function Notation Directions: For questions 17-22, find the function values using the given functions below.
f(x)=5x-20
g(x) = x2 + 5x-11
h( x) = I 2x + 7 I
17. /(6)
18. g(-3)
19. h(-8)
20. g(7)-15
21. -4 ? h(-13)
22. /(-1) + g(-2)
23. Given f(x) = 5- 3x, if f(x) = -19, find x.
24. Given g(x) = ~x -1, if g(x) = -16, find x.
2
Use the graph below for questions 25-28.
f(xl '\
'\
\ I\
\
I\
X
' '\
\ I\
\
25. Find /(-6). 26. Find /(O).
27. If f(x) = -5, what is x? 28. If J(x) = 4, what is x?
Topic s: Zeros
Directions: Identify the zeros of each function.
29.
ftxl
30.
fix)
I
I
.
? I
:/
I '
J
I
I
I
I
.1
_l.
31.
X
Directions: Find the zero(s) of each function algebraically.
32. f(x) = 8x - 16
33. f(x)=-10--2 x 3
f, ,: )
I/ \
I
\
I
\
'
I I
I\. J
Directions: Find the zero(s) of each function graphically.
34. f(x) = -x2 -lx-10
35. f(x) = x4 -8x3 + 5x2 + l 4x
Topic 6: Arithmetic Sequences
36. Write a formula for the sequence below, then find ais.
{5, 3, 1, -1, ...}
36. Write a formula for the sequence below, then find G34.
{-2, 5, 12, 19, ... }
Use for questions 37-38: Tabitha started working at a coffee shop making $8.75 per hour. Every six
months, she gets a $0.40 raise.
37. Write a formula to represent her hourly wage after each raise.
39. Find her hourly wage at 3 years.
Unit j. Test Study Guide
(Relations and Functions)
Name: Jll..e,p
I ? IO Date: lO
Per:
_
Topic 1: Relations & Functions
Directions: Identify the domain and range of each of relation. Then, determine whether the
relation is a function.
1.
2.
3.
X y
-4 8
{(-6, 4), (5,-1), (O, 3), (-2, 4)}
-3 1
o -5
-3 2
t -{, 1 Domain:
I -2 I O 1 ~
Range: \-\I 3 I '13
Function? '\ f.S
4.
Domain: t-1.\.-3,oJ
Range: \ .. 5 I \ ? 2 I ? ~
No Function?
5.
X
y
o+- ~2
'
-- 4- ..,:.-+ 3 4
9 5
Domain: t-G, ?31 O 1 216f
Range: \-3,L2\3l
Function? 'I{$
6.
X
y
- -~ -4
-1
-3
o
7
--
8
J Domain: ?-3 .-2 I 2, 4
t-s, Range:
-&.-\,o I t,7
Function? }\l? 7.
I
Domain: lD,'-Lq]
Range: '{ 2,.\ g J &.\ I 5 \
Function? 8.
~o ,,
/
~
I '
I
'
~
A\\ Domain:
'(/.?l #$
(i.)
Range: \.\=~
'\es Function?
/ /
V
I
Domain: X' -S Range: i ., -\ Function? 'ltS
Domain: \ -q ,-l, o, 71
t 3 Range: -?>, ~
~es Function?
9.
,r .....
I '
\
)
"" _,,
~s DfX Domain:
Range: -L\ l: '\ b 3 ND Function?
Topic 2.: Real World Graphs
Directions: Choose the graph that best represents each situation.
1 O. Corinna is riding a horse on a carousel.
Which graph best represents her
distance from the center of the ride in
a single rotation?
i
Cl
V
6
g E
gCueoli
GRAPH A
11. A cup of hot coffee cools down until it
reaches room temperature. Which
graph best represents the temperature
of the coffee?
!!
:i
?
?
Cli D.
E
~lii
GRAPH A
12. Mitch went for a hike. He got halfway
up the mountain and realized he had
dropped his compass. He turned
around and walked back. He found
the compass at the point he had started the hike. He picked it up, then
ouelii
hiked to the top of the mountain.
~
Which graph best represents the total
distance he hiked?
A
Time
GRAPH A
Time
Topic J: Equations as Functions/Graphing Functions using Tables
Directions: Complete the table, then graph the function.
13. y= -2x+5
X
y
o 5 , '
l 3
_,
3
5 -s
~?
' \
'
\
\
" \
. -
\
' \ \
lt
~
14. y= 23 x-1
X
y
-2 -~
o -1
2 2
4 5
GRAPH B
i
oGI
g E
GueoI
?-=
Time
GRAPH B
!
:i
~
Cl D.
E ~Cl
Time
GRAPH B
-=Coueli
?
Time
~
1'
V
I
/ I
.
V
, I
I/
I V
~
V
15. Find the range of the function y = ~ x + 17 4
when the domain is {-12, -4, 8}.
'X 1 '(
-\l. CZ
-i.t \'-\
f)2 -t-6(--3) -\l
~ q - \6 -1 \
= till
19. h(-8)
\ 2.l-i) t1 \
l \ -\" .1i1
\ -'\ l =BJ
20. g(7)-15
12.-\- 5(1) -\l -\S
=4'\ -t3S -\l -15
=?
21. -4 ? h(-13)
-L\ \ 2(-13) -t1 \
-a.\ \-lq \
\-1 l -"\U~) =
\?,
22. /(-1) + g(-2)
SC-\)-2.0 -4- (-2) 2 tS(-2.) ? li
= -s -20 + '.f -ID -li
=f42J
23. Given f(x} = 5 - 3x, if/{x) = -19, find x.
-\'1=5-3x
- 2'4 = -3.x
[)(=~1
Use the graph below for questions 25-28.
llxl
'\
' I\
'
?
' '
' '
'
% 24. Given g(x) = x - 1, if g(x) = -16, find x.
-Ilo =.52.-..x-1
!s..?-\S=fx ??
[x= -~}
25. Find /(-6).
7
26. Find /(O}.
-2
27. If f(x) =?5, what is x?
2
28. If f (x) = 4, what is x?
-4
Toplc s: Zeros
Directions: Identify the zeros of each function.
29.
Ox>
30.
ft1l
31.
hl
j
f
j
I
?
j I
j I
X -=--5
I ,
"
I
l
l
IJ
.L
)(:: l.-\ ,3)
?
'
j
\
I
",
J
'X= 10,2,1}
Directions: Find the zero(s) of each function algebraically.
32. f(x) = Bx-16
i~-\lo =O iX-=-llo
33. J(x) = -10--2 x
3
-10 - 16:- X -=-O
t~~2]
-.;.x=tc
3
l )(c:-\S
Directions: Find the zero(s) of each function graphically.
34. f(x)=-x2-7x-10
35. J(x) = x4 -8x3 + 5x2 + 14x
t=t-s. -2 J
t y._-::. -\I[) I 2 '1)
Topic 6: Arithmetic Sequences
36. Write a formula for the sequence below,
then find ais.
~,=s
{5, 3, 1, -1, ...}
?: ?2
?":: -2Ln-,) +s :: -2n t2-tS =r-2Vl-t7]
Q1c? = -llli)t 1
= t- 2~
36. Write a formula for the sequence below,
then find OJ4.
Q '-:. --2
{-2, 5, 12, 19, ...} cl =- 1
llv1 = 7 lr.-1)-2
= 1n-1-2
=-\1n-~J
I22~ ~"': 1(3'?4 = J
Use for questions 37-38: Tabitha started working at a coffee shop making $8.75 per hour. Every six
months, she gets a $0.40 raise.
37. Write a formula to represent her hourly wage after each raise.
CAV':: O .I.\O(n-\) -\o 9. \ 5
= o An -O.i,\ -t 9. IS
39. Find her hourly wage at 3 years. rr=-1,
E?\\. D.'-\ U,) ti. 1~
\SJ
=@Ar1 +?.151
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