Honors Algebra 1B Name ____________________________________ Per___

Unit 5 Test Review Functions, Exponents, Radicals, Arithmetic Sequences, & Geometric Sequences

1. Given ( ) 6 4f x x � find: a) ( 2)f � b) (3)f 2. Find the domain and range for each (interval notations). Determine which of the following are functions and explain your decision. a) {(0, 2), (2, 4), (0, -3), (5, 4)} b) {(-6, 5), (6, 5), (5, 2), (4, 2)}

c) d)

e)𝑓(𝑥) = −2𝑥 + 5 f)

Domain: ________________________ Range: ________________________ Function: Yes No Reason: ________________________

Domain: ________________________ Range: ________________________ Function: Yes No Reason: ________________________

Domain: ________________________ Range: ________________________ Function: Yes No Reason: ________________________

Domain: ________________________ Range: ________________________ Function: Yes No Reason: ________________________

Domain: ________________________ Range: ________________________ Function: Yes No Reason: _______________________

Domain: ________________________ Range: ________________________ Function: Yes No Reason: ________________________

Key

6C2 4 663 412 4 18 416 14

D 0,215 D 6,415,6R 3 2,43 R 2,5

The x value 0repeats one to one y

i lP lI i li l Ii l Ii l lto l ty

D 1,6 D fooR C3,3 R C2.25 approxdoesnotpassvertical passesverticallinetestlinetest

D oo D 5R C co R 1,2 4It's a linearequation theinputof 5 hasmore thanoneoutput

If

A

3. Use the graph on the right to answer the following questions. a. Write a story of what this graph might be showing. b. What is the average rate of change of elevation between 10 and 13 seconds? Leave answer as reduced fraction. c. What is the average rate of change of elevation between 0 and 15 seconds? Leave answer as reduced fraction d. State the domain and range for this graph in interval notations and inequalities. Domain: ________________________ Range: ________________________ 4. Simplify each expression so that there are no negative exponents.

a) b) ( )

c) d)

5. Simplify the radical expressions as much as possible

a) b) c)

answers will vary

1 62 m Yo I m felsec

1410 m Ya Is m Eftlsec

0,15 2,10

n m a2ab ab

x 252 y hnn n m

a

t8 bbbbb TFnnnmmmmmmmm5sn 9 2 2mm'VE

m Ya y0,10

45,441

3

as pn n m 2

320i 1m2 b

4m Eam2 5 b2h4 25 b8j 4aT

#6-11: State whether the following sequences are arithmetic, geometric, or neither, then state the common difference (d) or ratio (r) if applicable. 6. 6, 24, 96, 384, … 7. 3,14,25,36,... 8. 1, 2, 6, 24, …

9. 1,3,7,13,... 10. 1 1 1 1, , , ,......4 8 16 32

� � 11. -7, -16, -25, …

#12-13: State whether the following formulas are recursive or explicit. Write the first five terms for each sequence. Show all work. 12. � �2( ) 2 1f n n 13. f(n + 1)= 2 f(n) - 6 and f(1)= 2 for n≥1 #14-17: State whether each sequence is arithmetic or geometric then write a general term (explicit) formula for each sequence and find the 10th term.

14. 30, 27, 24, 21, … 15. 1 15, 1, , ,......5 25

� �

16. -2, -6, -18, … 17. -5, 16, 37, …

Yu tYtYtYGeometric Arithmetic neitherr 4 D

4neitherGeometric Arithmeticat D 92

Explicit 1 7 173149 Recursive 2 2 10 26 58f 1 24121 1 fu 2f 2 212121 7 f21 241 6 212 6 2f 3 2051 17 f 3 2fC2 6 2 2 6 10f 4 214171 31 fC41 2fC3 6 2410 6 26fest 215121 49 fcgy 2f 4 6 2126 6 58

Arithmetic Fcl 30 Geometric fcD 5 r ID 3 n l 3fan 30 3cm D Fcn 5 g30 3h 13 lo l

3h 133 Fcb b jFoo 340 133 3 0.00000256

Geometric 213 2 r 3 Arithmetic D 5,1 21n 1Fcn 263 fan 5 121cm D10 1Fao 2 3 5 121N 2192 3 21h 2639366 Fao 2l lo 26 184

O

#18-20: For each word problem below, write the explicit formula that represents the situation then answer the question. 18. You want to buy a new TV for $2100, but you have to save up over time. You save $25 in the first month, $35 the second month, $45 the third month and so on. How much will you saved in the 12th month? General term formula: ______________________ Answer: ___________________ 19. Edgar is getting better at math. On his first quiz he scored 57 points, then he scores 61 and 65 on his next two quizzes. If his scores continued to increase at the same rate, what will be his score on his 9th quiz? Show all work. General term formula: ______________________ Answer: ___________________ 20. Kevin is trying to reduce the amount of sugar he eats each day. In the first day, he allows himself to have a maximum of 50 grams. Each day he will reduce his maximum sugar intake by 3 grams. How many grams will he be allowed to have at the end of 2 weeks? General term formula: ______________________ Answer: ___________________

25,3745 fcD 25 d to

Fcn 25 110 n l Fcb loCl2 11525 10h 10 120 1510h 115 135

fch 10h 115 135

57,6465 Fcl 57d 4

Fh 57 14cm 1 Fca 4693 5357 14N 4 361 534h 153 89

Eh 4h 153 89 points

50,47 44,41 FCI 50 D 3fan 50 3cm l fCl4 34411 53

50 3h 13 421 533h 153 11

fin 3h 153 11 grams

21. If groceries now cost Mrs. Brooks $240 per week, she predicts that the cost will increase 10% per year due to inflation and her three growing boys eating more and more each year. Her oldest boy, John, is trying to figure out how much money will she be spending per week on groceries after 5 years. Below is his work – find and correct his mistake(s). Explain your reasoning.

1

5 1

( ) 240(.90)(5) 240(.90)

nf nf

�

�

She will be spending $157.46 22. A radioactive element has a half-life of 2 days. This means only half of the material is left after 2 days. If there are 10,240 grams present currently, then how much will be present at the beginning of the 16th day? General term formula: ______________________ Answer: ___________________ 23. Consider the arithmetic sequence 27, 13, -1, … a. Find an explicit rule for the sequence in terms of n. b. Find the 40th term. c. If the nth term is -841, find the value of n.

r 1101 1.1100 1101

Fcn 240 1.105 After 5 yearsFC6 240 1.1050 I n 6

240 1.1035

386.52

717 10240 L 16days n 8halflifecycles

n Ifch 10240 L2F 8 10240425 80

h Ifch 10240cL 80 grams

Fci 27 D 14

Fcn 27 14Ch l27 14h 11414h 141

fc4o 14C40 141 841 14h 141519 41 41

882 14h63 n

0

nth

27,13 I 841

24. Arithmetic sequences are modeled by __________functions and use the explicit formula: ___________________ Geometric sequences are modeled by ___________ function and use the explicit formula: ___________________ 25. Graphs of sequences are discrete or continuous? Explain. 26. Given the arithmetic sequence: 52, a, b, 64. Find the value of a•b.

linearfan FCI din l

In fci.phexponential

Discrete terms can only beintegers

a bFa 52 52 26,60,64FC4 64 56 60

Fcn fc den D 33607LFC4 fcDtdC4 l

64 52 1dB12 3d4 D

fL4tFc4 Fcc td 4 l64 52 t d 352 52

2 3d4 d

Answer Key: 1a. -16 1b. 14 2a. D: {0, 2, 5}

R: {-3, 2, 4} No Repeated X

2b. D: {-6, 4, 5, 6} R: {2, 5} Yes One X to one Y

2c. D: [-1, 5] R: [-3, 3] No Fails Vertical Line Test

2d. D: (-∞, ∞) R: [-2, ∞ ) Yes Passes Vertical Line Test

2e. D: (-∞, ∞) R: [-∞, ∞ ) Yes Linear

2f. D: {5} R: {1, 2, 4} No Repeated X values

3a. [stories will vary] 3b. 43

� ft / sec 3c. 25

� ft / sec 3d. Domain: [0,15] Range: [2,10]

4. a) b)

c) d)

5. a) 5𝑥√3𝑥 b) 9𝑎 𝑏 √2𝑏𝑐 c) 2𝑛𝑚 √4𝑛

6. geometric, r = 4

7. arithmetic, d = 11

8. neither

9. neither

10. geometric, r = -1/2

11. arithmetic, d = -9

12. explicit, -1, -7, -17, -31, -49

13. recursive, 2, -2, -10, -26, -58

14. ( ) 3 33f n n � �

f(10) = 3

15. 11( ) 5

5

n

f n�

§ · �¨ ¸© ¹

f(10) = 1 0.00000256

390625 � �

16. � � 1( ) 2 3 nf n � �

f(10) = -39366

17. ( ) 21 26f n n �

f(10) = 184

18. ( ) 25 10( 1)f n n � �

f(12) = $135

19. ( ) 57 4( 1)f n n � �

f(9) = 89 points

20. ( ) 3 53f n n � �

f(14) = 11 grams

21. two mistakes: correct answer is $386.52

22. 11( ) 10240

2

n

f n�

§ · ¨ ¸© ¹

f(8) = 80 grams

23a. ( ) 14 41f n n � �

23b. f(40) = -519 23c. n = 63 24. linear, ( ) (1) ( 1)f n f d n � �

exponential, 1( ) (1) nf n f r � �

25. discrete 26. 3360

Fcn fan 1 5

for fu 3

Write the first 4 termsFci 3

Fca 2 C 3 t 5

FC 3 3 2 C l t 5

Fc 4 11 2 3 5