sequences, functions & relations what do i need to know ......sequences, functions &...

Sequences, Functions & Relations Study Guide

SG-M67-Sequences, Functions, & Relations (SOL 7. 2 & 7.12) 2015-2016

What do I need to know for the assessment?

Sequences SOL 7.2

Functions & Relations SOL 7.12

Arithmetic and common difference Input, output, domain, and range Geometric and common ratio Vertical line test Sequence rules as algebraic expressions Determine the function given a table of

values or set of ordered pairs Finding missing terms Determine if a list of values for a given

relation is a function Complete or create a function table of

values Interpret a graph to determine if the

representation is a function Interpret a graph to determine a function

equation Interpret graphs for a given function

What are my resources to help me prepare for the assessment?

Class Notes & Independent Practice

Homework

Complete the practice problems on the pages that follow.

ASK questions if you need help before the assessment.

IXL Practice, 7th grade:

Sequences Functions

Q.1: Identify arithmetic and geometric sequences

V.1: Does (x, y) satisfy the equation

Q.2: Arithmetic Sequences V.5: Complete a table for 2 variables Q.3: Geometric Sequences V.6: Write a 2-variable equation Q.4: Number Sequences Mixed Review V.7: Identify the graph of an equation Q.5: Number Sequences Word Problems V.8: Graph a 2 variable equation Q.7: Write Variable Expressions for Arithmetic Sequences

V.9: Interpret graphs – word problems

V.10: Write an equation from a graph W.1: Find slope from a graph W.6: Write a linear function


Sequences Practice

1) If the sequence shown continues, what will be the 8th term?

54, 48, 42, 36,...

2) Which pattern follows the common ratio of 1

3 ?

A) 162, 54, 18, 6, 2 B) 120, 90, 60, 30, 10

C) 108, 36, 18, 9, 3 D) 105, 35, 32, 23, 20

3) Look at the table below and decide which rule Patrick’s pattern follows.

A) 𝑛 + 110 B) 11𝑛

C) 2𝑛 D) 𝑛2

4) Describe the sequence shown as an algebraic expression.

64, 16, 4, 1, . . .


5) Complete the table below.

Sequence Find the Common

Difference or Common

Ratio

Write the rule as an Algebraic

Expression

Is the sequence

Arithmetic or Geometric

Find the next 3 terms

−5, −8, −11, −14, …

120, 60, 30, 15, …

2.1, 2.2, 2.3, 2.4,…

31, 22, 13, 4, …

2, 12, 72, 432, …

−57, −50, −43, −36, …

4.8, 4.2, 3.6, 3.0…

625, 125, 25, 5, …

1, −5, 25, −125, …

−13

4, −1, −

1

4,1

2, …


Functions & Relations Practice

1) Given the table below, what is the rule as a function in two-variables (y=)?

Input 0 3 5 7 9 Output 0 6 10 14 18

2) Given the table below, what is the rule as a function in two-variables?

𝒙 -1 0 1 2 3 𝒚 1 2 3 4 5

3) Find the missing values to complete the function table.

𝒙 𝒚

0 9

2 11

4

8 17

20

4) Identify the domain and range for the following set.

{ (5,0), (6, 2), (7, 4), (8, 6), (9, 8) }

5) Determine if the following set is a function. Explain.

{ (−5, 3), (4, 3), (3, 2), (2, 0) }

6) Determine the domain and range for the following table of values.

Input Output −5 14 0 −6 3 −9 6 22 9 0


7) Which graph best represents the function 𝑦 = −2𝑥 + 4?

A) B)

8) Given the graph below, determine the equation.


9) Given the graph below, determine the equation.

10) Determine the equation for the given table of values.

Input Output

2 9

3 12

4 15

5 18

11) Determine the equation for the given table of values.

domain range

−2 0

−1 −2

0 −4

1 −6

2 −8


12) Which appears to be the rule in the equation graphed?

A) The domain is two more than the range.

B) The range is twice the domain.

C) The range is two less than the domain.

D) The domain is two less than the range.

13) Lucy is helping her father input his company’s files into a new computer database. Her

father agreed to pay her $5 for the first file and $2 for each files after that.

Which equation, where 𝑝 stands for her pay, and 𝑓 stands for the number of files

completed, could be used to determine Lucy’s pay?

A) 𝑝 = 2𝑓 + 5 B) 𝑝 = 5𝑓 + 2𝑓

C) 𝑝 = 2(𝑓 + 1) + 5 D) 𝑝 = 2(𝑓 − 1) + 5

14) Choose each ordered pair that is NOT a point on the graph of 𝒚 =𝟏

𝟑𝒙

A) (−6, 2) B) (12, 3) C) (−3, −1)

D) (24, 8) E) (−15, −5) F) (0, 1)


15-18: Determine if the following are functions and justify your answer.

15)

𝒙 7 17 27 7 47 57

𝒚 9 8 7 6 5 4

16) {(4, 5) (6, 5) (7, 5) (8, 5)} 17) {(−1, 2) (3, 5) (−1, 8) (11, 11)}

18) 19)

20) Which table contains only the points that lie on the line represented by 𝒚 =𝟔

𝟓𝒙 − 𝟐 ?

A) 𝑥 𝑦

−1 −0.8

5 4

B) 𝑥 𝑦

−2 −0.4

4 2.2

C) 𝑥 𝑦

−2 −4.4

4 2.8

D) 𝑥 y

−1 −3.2

5 3.2


21-24: Graph the following functions.

21) 𝑦 = 3𝑥 − 2 22) 𝑦 = −1

2𝑥 + 3

23) 𝑦 = 4𝑥 + 1 24) 𝑦 = −2𝑥 − 4


Answer Key

Sequences Practice

1) 12

2) A

3) D

4) 𝑛

4

5)

Sequence Find the Common

Difference or Common Ratio

Write the rule as an Algebraic

Expression

Is the sequence Arithmetic or

Geometric

Find the next 3 terms

−5, −8, −11, −14, …

𝑑 = −3 𝑛 + (−3) A −17, −20, −23

120, 60, 30, 15, … 𝑟 =

1

2

𝑛

2𝑜𝑟 0.5𝑛 G 7.5, 3.75, 1.875

2.1, 2.2, 2.3, 2.4,… 𝑑 = 0.1 𝑛 + 0.1 A 2.5, 2.6, 2.7

31, 22, 13, 4, … 𝑑 = −9 𝑛 + (−9) A −5, −14, −23

2, 12, 72, 432, … 𝑟 = 6 6𝑛 G 2592, 15552, 93312

−57, −50, −43, −36, …

𝑑 = 7 𝑛 + 7 A −29, −22, −15

4.8, 4.2, 3.6, 3.0…

𝑑 = −0.6 𝑛 + (−0.6) A 2.4, 1.8, 1.2

625, 125, 25, 5, … 𝑟 =1

5

𝑛

5𝑜𝑟 0.2𝑛 G

1,1

5,

1

25

1, −5, 25, −125, … 𝑟 = −5 −5𝑛 G −625, 3125, −15625

−13

4, −1, −

1

4,1

2, … 𝑑 =

3

4 𝑛 +

3

4

A 1

1

4, 2, 2

3

4


Functions and Relations Practice

1) 𝑦 = 2𝑥

2) 𝑦 = 𝑥 + 2

3) 𝑦 = 13 𝑎𝑛𝑑 𝑥 = 11

4) domain: 5, 6, 7, 8, 9 range: 0, 2, 4, 6, 8

5) The set is a function since each member of the domain has only one partner in the

range.

6) Domain: −5, −, 3, 6, 9 range: 14, −6, −9, 22, 0

7) B

8) 𝑦 = −𝑥 + 3

9) 𝑦 = 2𝑥 − 2

10) 𝑦 = 3𝑥 + 3

11) 𝑦 = −2𝑥 − 4

12) C

13) D

14) A, B, F

15) Not a function since 7 in the domain has two partners in the range (2 and 8)

16) The set is a function since each member of the domain has one partner in the range.

17) Not a function since -1 in the range has two partners in the range (2 and 8)

18) Not a function, does not pass the vertical line test

19) The graph is a function as it does pass the vertical line test.

20) C

21) 𝑦 = 3𝑥 − 2 22) 𝑦 = −1

2𝑥 + 3


23) 𝑦 = 4𝑥 + 1 24) 𝑦 = −2𝑥 − 4

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