Directions: Fill in the Vocabulary Self-Awareness Chart Below

Unit 6, Activity 1, Function Vocabulary

Directions: Fill in the vocabulary self-awareness chart below. In this chart you are to analyze your own comfort level with each of the terms listed. First, you will analyze your comfort level (in the left-hand column) before going through some activities which deal with the topics listed. Write definitions and examples for the terms you may know. Later, after going through the activities, you will assess yourself again (using the right-hand column).

If you fully understand a term, place a + sign in the chart and write its definition below the chart. If you have limited understanding of a particular term or topic but still need more assistance, place an O in the chart. If you have no understanding of a particular term or topic, place a – sign in the chart.

Comfort Level Before Activity
+, 0, or - / Vocabulary Term / Definition / Example / Comfort Level After Activity
+, 0, or -
Relation
Function
Domain
Range
Independent variable
Dependent variable

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Unit 6, Activity 2, Is it a Function?

For each relation provided below, determine if the relation is a function. Write YES or NO in the blank provided. If the relation is not a function, explain why.

1. ______2. ______

Age / 14 / 15 / 16 / 16
GPA / 3.6 / 3.3 / 3.0 / 2.8

3. ______4. ______

x / 7 / 4 / -3 / 5
y / 4 / 6 / 3 / 4
x / 7 / 4 / 5 / 5
y / 4 / 6 / 3 / 4

5. ______6. ______

Age (months) / 2 / 9 / 16 / 23
Weight
(pounds) / 15 / 24 / 30 / 35

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Unit 6, Activity 2, Is it a Function? with Answers

For each relation provided below, determine if the relation is a function. Write YES or NO in the blank provided. If the relation is not a function, explain why.

1. _NO______2. _N0____

It’s not a function since the input 0 It’s not a function since the age of 16

corresponds to two different outputs.corresponds to two different GPAs.

Age / 14 / 15 / 16 / 16
GPA / 3.6 / 3.3 / 3.0 / 2.8

3. __YES____4. __NO___

It’s not a function since the x-value,

5, corresponds to two outputs.

x / 7 / 4 / -3 / 5
y / 4 / 6 / 3 / 4
x / 7 / 4 / 5 / 5
y / 4 / 6 / 3 / 4

5. _YES____6. _YES____

Age (months) / 2 / 9 / 16 / 23
Weight
(pounds) / 15 / 24 / 30 / 35

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Unit 6, Activity 5, Real Life Functions

Directions: Work with a partner on the problems below. Answer all the questions based on the presented situation.

The initial start-up costs for a company to manufacture data recorders are $15,000, while each recorder costs $4 to manufacture.

a.In this example, what are the dependent and independent variables in real-life terms?

b.Write the equation using function notation where x represents the number of recorders and represents the cost of manufacturing x recorders.

c.Graph the relationship given, and then determine the domain and range of this real-life relationship.

d.Is this relationship a function? Explain.

e.What is the real-world meaning of the y-intercept of the graph?

f.What is the real-world meaning of the slope associated with this graph?

g.Explain what the value is and the meaning of in real-world terms.

h.Explain what x value will result in. Explain how you obtained your answer.

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Unit 6, Activity 5, Real Life Functions with Answers

Directions: Work with a partner on the problems below. Answer all the questions based on the presented situation.

The initial start-up costs for a company to manufacture data recorders are $15,000, while each recorder costs $4 to manufacture.

a.In this example, what are the dependent and independent variables in real-life terms?

Solution: Thecostdepends on the number of recorders produced; thus, cost is dependent and number of recorders is independent.

b.Write the equation using function notation where x represents the number of recorders and represents the cost of manufacturing x recorders.

Solution:

c.Graph the relationship given, and then determine the domain and range of this real-life relationship.

Solution: See student graphs. Domain is since you cannot have a negative number of recorders, and Range is.

d.Is this relationship a function? Explain.

Solution: Yes, this is a function since for each input value (number of recorders), there is only one output value (cost of producing x number of recorders).

e.What is the real-world meaning of the y-intercept of the graph?

Solution: The y-intercept for this graph is $15,000, which represents the fixed cost associated with producing 0 recorders.

f.What is the real-world meaning of the slope associated with this graph?

Solution: The slope is $4 per recorder—the variable cost of producing each recorder.

g.Explain what the value is and the meaning of in real-world terms.

Solution: and it represents the cost of producing 100 recorders.

h.Explain what x value will result in. Explain how you obtained your answer.

Solution: The x value associated with a cost of $95,000 is. Students can obtain this value in different ways. Check student work.

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Unit 6, Activity 6, Arithmetic Number Patterns

Directions: Find a pattern for each sequence and show the next two terms. Then answer the questions that follow.

1, 7, 13, 19, 25, _____, ______

Describe the pattern in words.

Create a table of input/output values comparing the term (input) and the number (output) for this situation.

On graph paper, graph the relationship between the term and output number. Is the relationship linear or non-linear?

Create a function model you can use to represent the relationship between the term and output number.

Use the function model you created to determine the 1000th term in the number sequence. Show how you got your answer.

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Unit 6, Activity 6, Arithmetic Number Patterns with Answers

Directions: Find a pattern for each sequence and show the next two terms. Then answer the questions that follow.

1, 7, 13, 19, 25, _31__, __37__

Describe the pattern in words.

Each succeeding number is adding 6 to the previous number.

Create a table of input/output values comparing the term (input) and the number (output) for this situation.

Term (input) / 1 / 2 / 3 / 4 / 5
Number (output) / 1 / 7 / 13 / 19 / 25

On graph paper, graph the relationship between the term and output number. Is the relationship linear or non-linear?

See student graphs; the relationship is linear.

Create a function model you can use to represent the relationship between the term and output number.

f(x) = 6x - 5

Use the function model you created to determine the 1000th term in the number sequence. Show how you got your answer.

f(1000)= 6(1000) – 5 = 6000 – 5 = 5995

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Unit 6, Activity 7, Geometric Patterns

Directions: Find a pattern for each sequence. Use the pattern to determine the next two terms. Then determine the constant ratio which produced the pattern. Afterward answer the questions that are presented.

5, 10, 20, 40, _____, ______Ratio: ______

Create a table of input/output values comparing the term (input) and the number (output) for this situation.

On graph paper, graph the relationship between the term and output number. Is the relationship linear or non-linear?

Create a function model you can use to represent the relationship between the term and output number (with our without a graphing calculator).

Use the function model you created to determine the 10th term in the number sequence. Show how you got your answer.

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Unit 6, Activity 7, Geometric Patterns with Answers

5, 10, 20, 40, _____, ______Ratio: ______

Create a table of input/output values comparing the term (input) and the number (output) for this situation.

Term (input) / 1 / 2 / 3 / 4 / 5
Number (output) / 5 / 10 / 20 / 40 / 80

On graph paper, graph the relationship between the term and output number. Is the relationship linear or non-linear?

See student graphs; relationship is non-linear (or exponential).

Create a function model you can use to represent the relationship between the term and output number (with our without a graphing calculator).

Use the function model you created to determine the 10th term in the number sequence. Show how you got your answer.

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Unit 6, Activity 8, Patterns in Tables

Directions: Look at the table shown below. Answer the following questions related to this table:

Input (Term #) / 1 / 2 / 3 / 4 / 5 / ----- / 300 / ----- / nth Term
Output (Value) / 6 / 7 / 8 / 9 / 10 / ---- / -----

What relationship do you notice between the input (term number of the pattern) and the output (value of the term)? Explain in words what you notice.

What output value is associated with the input of 300? In other words, what will be the value of the 300th term in the pattern? Explain how you got your answer.

If you wanted to know the output value for the nth term, what expression could be written? In other words, what is the value of the nth term in the pattern?

Use the formula for the nth term to find the 500th term.

Find the values for the 300th term and the nth term in the table then explain how you got your answers.

Input
(term number) / 1 / 2 / 3 / 4 / 5 / ----- / 300 / ----- / n
Output (Value) / 6 / 12 / 18 / 24 / 30 / ----- / -----

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Unit 6, Activity 8, Patterns in Tables with Answers

Directions: Look at the table shown below. Answer the following questions related to this table:

Input (Term #) / 1 / 2 / 3 / 4 / 5 / ----- / 300 / ----- / nth Term
Output (Value) / 6 / 7 / 8 / 9 / 10 / ---- / -----

What relationship do you notice between the input (term number of the pattern) and the output (value of the term)? Explain in words what you notice.

Solution: The output value is always 5 more than the input value.

What output value is associated with the input of 300? In other words, what will be the value of the 300th term in the pattern? Explain how you got your answer.

Solution: The value of the 300th term will be 305 since the value is 5 more than the term number.

If you wanted to know the output value for the nth term, what expression could be written? In other words, what is the value of the nth term in the pattern?

Solution: The value of the nth term is “.”

Use the formula for the nth term to find the 500th term.

Solution: The 500th term would be 505.

Find the values for the 300th term and the nth term in the table then explain how you got your answers.

Input
(term number) / 1 / 2 / 3 / 4 / 5 / ----- / 300 / ----- / n
Output (Value) / 6 / 12 / 18 / 24 / 30 / ----- / -----

Solution: The pattern appears to be that the output value is found by multiplying the term number by 6 to get each term value. Therefore, the 300th term will be () or 1800.

The nth term will be “6n”.

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Unit 6, Activity 9, Making a Table

Josh created the following number pattern: -4, -3, -2, -1, 0, 1, ….

Fill in the table shown below with the correct information,

Input
(term number) / ------/ ------
Output (Value) / ------/ ------

Find out the 300th term. Show or explain how you came up with your answer.

Write an expression for the nth term.

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Unit 6, Activity 9, Making a Table with Answers

Josh created the following number pattern: -4, -3, -2, -1, 0, 1, ….

Fill in the table shown below with the correct information,

Input
(term number) / 1 / 2 / 3 / 4 / 5 / ----- / 300 / ----- / N
Output (Value) / -4 / -3 / -2 / -1 / 0 / ----- / 295 / ----- /

Find out the 300th term. Show or explain how you came up with your answer.

Since the pattern shown seems to indicate that the output value is found by subtracting 5 from the input term, the 300th term would be found by subtracting 5 from 300: 300 – 5 = 295.

Write an expression for the nth term.

n - 5

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Unit 6, Activity 11, All About Patterns

Directions: With your group, answer the questions that follow. Be prepared to discuss the solution in front of the class.

Problem 1: Look at the data table below and use it to answer the following questions:

Term / 1 / 2 / 3 / 4 / 5 / 6 / 7
Value / 5 / 7 / 9 / 11

a.Find the missing values that belong in the table.

b.Describe the pattern in words.

c.Write an equation to represent the value of the nth term.

d.Using the equation you found for the nth term, find the value for the 200th term.

e.Looking at the data, does the data appear to be linear? Explain.

f.Using a graphing calculator, create a scatter plot of the data. Use the scatter plot to determine if the data is linear or not. Is it linear?

Problem 2: Use the data in the table to answer the following questions:

Term / 1 / 2 / 3 / 4 / 5 / 6 / 7
Value / 1 / 4 / 9 / 16

a.Find the missing values that belong in the table.

b.Describe the pattern in words.

c.Write an equation to represent the value of the nthterm.

d.Using the equation you found for the nth term, find the value for the 200th term.

e.Looking at the data, does the data appear to be linear? Explain.

f.Using a graphing calculator, create a scatter plot of the data. Use the scatter plot to determine if the data is linear or not. Is it linear?

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Unit 6, Activity 11, All About Patterns with Answers

Directions: With your group, answer the questions that follow. Be prepared to discuss the solution in front of the class.

Problem 1: Look at the data table below and use it to answer the following questions:

Term / 1 / 2 / 3 / 4 / 5 / 6 / 7
Value / 5 / 7 / 9 / 11 / 13 / 15 / 17

a.Find the missing values that belong in the table.

b.Describe the pattern in words.

Solution: For each of the next numbers in the pattern, the value is increased by 2. Looking at the relationship between the term number and the value, a pattern develops—if the term number is doubled then 3 is added to this value, we get the output value.

c.Write an equation to represent the value of the nth term.

Solution: Value = (where n is the term number)

d.Using the equation you found for the nth term, find the value for the 200th term.

Solution: 403

e.Looking at the data, does the data appear to be linear? Explain.

The data is linear since the ratio of the change in term and change in value is constant (slope is constant value of 2).

f.Using a graphing calculator, create a scatter plot of the data. Use the scatter plot to determine if the data is linear or not. Is it linear?

Solution: Graph is linear.

Problem 2: Use the data in the table to answer the following questions.

Term / 1 / 2 / 3 / 4 / 5 / 6 / 7
Value / 1 / 4 / 9 / 16 / 25 / 36 / 49

a.Find the missing values that belong in the table.

b.Describe the pattern in words.

Solution: The pattern shows that the term number is being squared to get the output value.

c.Write an equation to represent the value of thenth term.

Solution: Value =

d.Using the equation you found for the nth term, find the value for the 200th term.

Solution: 40,000

e.Looking at the data, does the data appear to be linear? Explain.

Since the slope is not constant, the data is not linear.

f.Using a graphic calculator, create a scatter plot of the data. Use the scatter plot to determine if the data is linear or not. Is it linear?

Solution: Graph is non-linear.

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