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: Domain: Domain:

Range: Range: Range:

Function? Function? Function?

4. 5. 6. X y X y

~ 2 -4 o ---- ..-e---->- 3 -1 -3 ' 4-

- 4 o , 8 9 -- 5 7

Domain: Domain: Domain:

Range: Range: Range:

Function? Function? Function?

7. 8. .,, 9. V

V I /

\ ,, / ' , / I \

~ I / ' I ' ' V ,, ' ,,

I I I \ J

I ' ' / I

~ .. Domain: Domain: Domain:

Range: Range: Range:

Function? Function? 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. GRAPH A GRAPH B

Which graph best represents her distance from the center of the ride in a single rotation? - ;¡; l! e ê

GI GI u u E E _g _g GI GI u u e e .E ~ "' ë ë

Time Time

11. A cup of hot coffee cools down until it GRAPH A GRAPH B reaches room temperature. Which graph best represents the temperature of the coffee?

GI GI :5 :5 ô ô ;¡; ;¡; 0. 0. E E GI .... GI ....

Time Time

12. Mitch went for a hike. He got halfway GRAPH A GRAPH B 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 GI started the hike. He picked it up, then u u e .E e

hiked to the top of the mountain. "' .E ë "'

Which graph best represents the total ë

distance he hiked?

Time Time

Topic 3: Equations as Functions/Graphing Functions using Tables Directions: Complete the table, then graph the function. 13. y= -2x+ 5 3 14. y =-x-1 '~ 2

X y X y

o -2 - , - , l o 3 2

5 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. 25. Find /(-6). f(xl

'\ '\

26. Find /(O). \ I\

\ I\ X

27. If f(x) = -5, what is x? ' '\

\ 28. If J(x) = 4, what is x? I\

\

Topic s: Zeros Directions: Identify the zeros of each function. 29. ftxl 30. fix) 31. f,,:)

I

:/

I I ' . X I/ \ ' ¡ J I \ I I I I I

\ I

I I\. J I

.1 _l.

Directions: Find the zero(s) of each function algebraically. 32. f(x) = 8x - 16 33. 2 f(x)=-10--x

3

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 39. Find her hourly wage at 3 years.

wage after each raise.

Unit j. Test Study Guide (Relations and Functions)

Name: Jll..e,p Date: IO I lO ß 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

Domain: t -{, I -2 I O 1 ~ 1 Domain: t-1.\.-3,oJ Domain: t-G, •31 O 1 216f Range: \-\I 3 I '13 Range: \ .. 5 I \ ¡ 2 I Î ~ Range: \-3,L2\3l Function? '\ f.S Function? No Function? 'I{$ 4. 5. 6.

X y X y

~2 -4 o+- ---~ ..,:.-+ 3 4- -1 -3 ' - 4 o 8 9 - 5 -- 7

Domain: Î-3 .-2 I 2, 4 J Domain: lD,'-Lq] Domain: \ -q ,-l, o, 71 Range: t-s, -&.-\,o I t,7 Range: '{ 2,.\ g J &.\ I 5 \ Range: t -?>, ~ 3 Function? }\lô Function? ~o Function? ~es 7. 8. ,, 9.

/ ~

I ,r .....

/ I ' ' / I V

I

' \ )

"" _,,

I

~

Domain: A\\ '(/.ßl #$ (i.) Domain: X' -S Domain: DfX ~s Range: \.\=~ Range: i ., -\ Range: -L\ l: '\ b 3 Function? '\es Function? 'ltS Function? ND

Topic 2.: Real World Graphs Directions: Choose the graph that best represents each situation. 1 O. Corinna is riding a horse on a carousel. GRAPH A GRAPH B

Which graph best represents her distance from the center of the ride in a single rotation? i i

Cl GI V o

6 E E g g Cli GI u u e e o o g -= ë

Time

11. A cup of hot coffee cools down until it GRAPH A GRAPH B reaches room temperature. Which graph best represents the temperature of the coffee?

!! ! :i :i ß ë ~ Cli Cl D. D. E E lii Cl ~ ~

Time Time

12. Mitch went for a hike. He got halfway GRAPH A GRAPH B 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 lii Cli started the hike. He picked it up, then u u e e hiked to the top of the mountain.

o o ~ -=

Which graph best represents the total ë

distance he hiked?

A Time Time

Topic J: Equations as Functions/Graphing Functions using Tables Directions: Complete the table, then graph the function. 13. y= -2x+5 3 1' ~¡

14. y= 2x-1 ~

' V \ I ' X y X y / \

o 5 \ -~ I , " . -2 . ' \ - V l 3 o -1 I \

' , 3

_, 2 2 I/ \

5 -s \ 4 5 I V

lt ~ ~ V

15. Find the range of the function y = ~ x + 17 16. Find the range of the function y= -x2 - 3x

4 when the domain is {-5, O, 2}. when the domain is {-12, -4, 8}.

X \l 'X 1 '( -s R:: 1-,0, o} -\l. CZ -IO f<:- \Î 1 \&\I,;~} o -i.t \'-\ o

i ,23 l -IO

Topic 4: Function Notation Directions: For questions 17-22, find the function values using the given functions below.

/(x) = Sx-20 g(x)=x2+5x-11 h(x)=l2x+71

17. /(6) 18. g(-3) 19. h(-8)

5Uo) - 2.0 l-3>)2 -t-6(--3) -\l \ 2.l -i) t1 \

=I@] ~ q - \6 -1 \ \ -\" .1i1 l = till \ -'\ l =BJ

20. g(7)-15 21. -4 · h(-13) 22. /(-1) + g(-2)

12.-\- 5(1) -\l -\S -L\ \ 2(-13) -t1 \ SC-\)-2.0 -4- (-2) 2 tS(-2.) · =4'\ -t3S -\l -15 -a.\ \-lq \ = -s -20 + '.f -ID -li =® -"\U~) = \-1 \¿, l =f42J 23. Given f(x} = 5 - 3x, if /{x) = -19, find x. 24. Given g(x) = % x - 1, if g(x) = -16, find x.

-\'1=5-3x -Ilo =.5...x-1 - 2'4 = -3.x 2-

!..•-\S=fx ·¼ [)(=~1 s [x= -~}

Use the graph below for questions 25-28. 25. Find /(-6). llxl 7 '\

26. Find /(O}. ' I\ -2 ' • 27. If f(x) =·5, what is x?

' ' 2 ' 28. If f (x) = 4, what is x? ' ' -4

li

Toplc s: Zeros Directions: Identify the zeros of each function. 29. Ox> 30. ft1l 31. hl

j

f

j

I I , • " •

j ' I I l j

\ I

j ", I l

IJ .L J

X -=--5 )(:: l.-\ ,3) 'X= 10,2,1} Directions: Find the zero(s) of each function algebraically. 32. f(x) = Bx-16 33. 2 J(x) = -10--x

i~-\lo =O 3 -10 - 1:- X -=-O iX-=-llo 6

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 y._-::. t -\I[) I 2 '1) Topic 6: Arithmetic Sequences 36. Write a formula for the sequence below, 36. Write a formula for the sequence below,

then find ais. ~,=s then find OJ4. Q '-:. --2 {5, 3, 1, -1, ... } ò: ·2

{-2, 5, 12, 19, ... } cl =- 1 ª":: -2Ln-,) +s Q1c¡ = -llli)t 1 llv1 = 7 lr.-1)-2 ~"': 1(3'Û4 :: -2n t2-tS = t--2~ = 1n-1-2 = I22~ J =r-2Vl-t7] =-\1n-~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 39. Find her hourly wage at 3 years. rr=-1,

wage after each raise. D.'-\ U,) ti. 1~ CAV':: O .I.\O(n-\) -\o 9. \ 5 E·\\. \SJ = o An -O.i,\ -t 9. IS =@Ar1 +ß.151