Module 4 Learning Guide: An Introduction to Functions
Directions: Use this notes sheet to record important definitions and ideas for each lesson as you work through the Module 4 notes. Take your time and do your best!
Lesson 1: All About Functions

Define relation.

The 4 ways a relation can be represented are
____________________________________,
_____________________________________,
____________________________________, and
___________________________________________.

Define domain.

Define range.
 What’s the most common way to order the domain and range in a set?
Use the Relation from Page 1 in the notes to answer the following questions:

Draw a mapping of the relation.

Graph the relation.
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Module 4 Learning Guide: An Introduction to Functions
Lesson 1 continued: All About Functions

Write the relation in a table. x y

Write the domain.

Write the range.

Define function.

Draw an example of a mapping of a relation that is a function and is not a function.
Is A Function Is NOT a Function
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Module 4 Learning Guide: An Introduction to Functions
Lesson 1 continued: All About Functions

Explain how the vertical line test is used to determine if a relation is a function.

Define inverse of a relation.

Give an example of a function and its inverse where the inverse is also a function.

Give an example of a function and its inverse where the inverse is not a function.

Give an example of a relation that is not a function and its inverse where the inverse is a function.

Explain how you find the inverse of an equation.

Show all the steps to find the inverse of the first equation on Page 5 of the notes.

What is the inverse of a vertical line?

The inverse of y = -5 is ____________________.
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Module 4 Learning Guide: An Introduction to Functions
Lesson 2: Evaluating Functions

Define Function Rule.

Define Function Notation.

What is f(x)?

Is the domain input or output? ____________________________________

Is the range input or output? _____________________________________

Name the four ways that we can combine functions.
1. ____________________
2. ____________________
3. ____________________
4. ____________________

Name the four steps to find an inverse.
1. ______________________________________________________
2. ______________________________________________________
3. ______________________________________________________
4. ______________________________________________________
 How can we tell if an equation’s inverse is a function?
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Module 4 Learning Guide: An Introduction to Functions
Lesson 3: Arithmetic Sequences

Define sequence.

Define term.

Define arithmetic sequence.

Define common difference.

Copy the Key Point located on Page 2.
 Write an example of an arithmetic sequence and give it’s common difference.

Write an example of a sequence that is not an arithmetic sequence.

Define recursive formula.

Write the Recursive Formula for an Arithmetic Sequence.
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Module 4 Learning Guide: An Introduction to Functions
Lesson 3 continued: Arithmetic Sequences

Write how to use the formula as shown in the video on Page 4.

What do you need to write a recursive formula for an arithmetic sequence?
 Write an example of an arithmetic sequence and it’s recursive formula.

Write the Recursive Formula in Function Notation for an Arithmetic Sequence.
 Write an example of an arithmetic sequence and it’s recursive formula in function notation.

Define explicit formula.

Give an example of an arithmetic sequence and its explicit formula.
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Module 4 Learning Guide: An Introduction to Functions
Lesson 3 continued: Arithmetic Sequences

Write the steps to write an explicit formula and use to find a specific term:

Write an example of an arithmetic sequence using the explicit formula.
Lesson 4: Geometric Sequences

Define geometric sequence.

Define common ratio .

Why is the change between terms called a common ratio instead of a common difference?

Give an example of a geometric sequence and write the common ratio.

Write the Recursive formula for a Geometric Sequence.

Write an example showing all the steps to find a specific term using the recursive formula.
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Module 4 Learning Guide: An Introduction to Functions
Lesson 4 continued: Geometric Sequences

Show the steps to find the first 4 terms of the geometric sequence given the recursive formula NEXT = NOW

2, starting at 4.

Explain how to write a recursive formula for a geometric sequence.

Write the Recursive Formula in Function Notation for a Geometric Sequence.

Show how to find the first 4 terms of sequence using function notation.

Write the Explicit Formula for a Geometric Sequence.

Write an example of a Geometric Sequence in Explicit form. Identify the first term and common difference.
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Module 4 Learning Guide: An Introduction to Functions
Lesson 4 continued: Geometric Sequences

Why is the order of operations important when simplifying geometric sequences in explicit form?

Explain how to write an explicit formula for a geometric sequence.

Give an example of a geometric sequence. Write the explicit form of the sequence and use to find 15 th term showing all work.
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