Name______Teacher______

Date ______Period ______

Math 3 Unit 1
Intro to Functions
Guided Notes Packet

In order to successfully complete the guided notes section of this packet, you will need to pay close attention to today’s class lecture.

Relations and Functions

Based on our previous notes and class discussions we know that a relation is a set of ______or ______, often written as ______. In this case the X corrdinate is our Input and the Y coordinate is our Output. Prior to graphing a relation we can represent a relation as a ______diagram. For example, the relation can be represented as :

By looking at this mapping diagram, we can automatically tell that this is a ______and NOT a ______. We know this because there are two ______X values. The lines in the middle connect each ______with their respective ______. This relation can also be represented as a graph:

The ordered pairs (coordinates) for this relation again are
( , ) , ( , ) , ( , ) , ( , ) , ( , ) .

FUNCTIONS

A FUNCTION is a RELATION in which each input has only ______output !!!

A FUNCTION is a RELATION in which each input has only ______output !!!

A FUNCTION is a RELATION in which each input has only ______output !!!

Line Vertical and Horizontal Line Tests for Graphs

To determine whether ______is a function of ______, given a graph of a relation, use the following criteria. If every ______you can draw goes through only 1 point, y is a function of x. if you can draw one vertical line that goes through 2 points, y is not a ______. This is called the ______.

Example 1: In the following graph, Y is a function of X.

This function (circle one) passes / fails the vertical line test.

Example 2: In the following graph, Y ______a function of X.

If everyhorizontal lineyou can draw passes through only 1 point,xis a function ofy. If you can draw a horizontal line that passes through 2 points,______a function ofy. This is called ______.

Practice Problems

  1. Make a mapping diagram for the following relation: .

Mapping Diagram

What are the coordinates ? _____ , ______, ______, ______.

Is this a function? ______.

Using the vertical line test, determine if the graph above shows a relation, a function, both a relation and a function, or neither a relation nor a function.

A. neither a relation nor a function
B. relation only
C. both a relation and a function
D. function only

3.

Which of these graphs represents a function?

A.Z

B.X

C.W

D.Y

3. Which of these t-tables represents a function?

A.W
B. Y
C. Z
D. X

B.

6. Do the ordered pairs below represent a relation, a function, both a relation and a function, or neither a relation nor a function?

(-2,-1) , (1,-4) , (7,-10) , (8,-11)

A. neither a relation nor a function
B. both a relation and a function
C. relation only
D. function only

7. Determine whether this picture is an example of a function, relation, function and relation, or neither relation nor function.

A. function and relation
B. function only
C. relation only
D. neither function nor relation

8. Which relation diagram represents a function?

ZX

WY

A. Z
B. X
C. W
D. Y

9. Think about the vertical line test and answer the following question. Would a vertical line be a relation, a function, both a relation and a function, or neither a relation nor a function?

A. function only
B. both a relation and a function
C. neither a relation nor a function
D. relation only

10. Do the ordered pairs below represent a relation, a function, both a relation and a function, or neither a relation nor a function?

(-4,-3) , (1,-8) , (-4,-14) , (9,-16)

A. function only
B. both a relation and a function
C. neither a relation nor a function
D. relation only