unit 1: functions lesson 1: relations and functions learning goals: i can determine if a relation is...
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Unit 1: Functions
Lesson 1: Relations and Functions
Learning Goals:
I can determine if a relation is a function
Unit 1: Functions
Lesson 1: Relations and Functions
So far, we have seen mathematical relationships written like this:
•y = 3x + 1•y = 2x2 -2•y = x2
•y = 5x•Etc, etc.
These examples are relations: They are rules describing the relationship between the dependent and independent variables.
The Dependent Variable is:The Independent Variable is:
A relation is a connection (or relationship) between two sets of numbers, such as height vs. time or cost vs. weight
Unit 1: Functions
Lesson 1: Relations and Functions
Example: The height, h, of an object thrown up in the air is dependent on the time, t. “h” is dependent on “t”, therefore h is the dependent variable and t is the independent variable.
Unit 1: Functions
Lesson 1: Relations and Functions
These examples represent function notation and are read as, “ f of x”, or “f at x”.
Unit 1: Functions
Lesson 1: Relations and Functions
Function notation represents a relation where there is only one unique value of the function (f) for any value of x.In other words, each x-value (independent variable) has only one y-value (dependent variable)
Unit 1: Functions
Lesson 1: Relations and Functions
How do you know whether something is a function?
• If you put in a value for “x” and there is only one value for “y” it is a function.
• If you put in a value for “x” and get more than one value for “y”, it is not a function.
Example:
Camary
Rav 4
Yaris
Prius
Toyota
INPUT OUTPUT
CamaryVenzaRav 4SiennaYarisCorollaPrius
Toyota
INPUT OUTPUT
Unit 1: Functions
Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
A function can be represented by:
1) A Table of Values2) A Set of Ordered Pairs3) A Mapping Diagram4) A Graph5) An Equation
Unit 1: Functions
Lesson 1: Relations and Functions
Table of Values: It is a function if each x-value only
corresponds to one y-value
x y-2 3-1 20 1-1 0
x y1 53 67 82 8
Unit 1: Functions
Lesson 1: Relations and Functions
Ordered Pairs: It is a function if for each x-
value there is only one y-value
f = {(1,-4), (2, 5), (8, 9), (0, 6)}
g = {(1, -3), (2, -3), (3, 0), (2, 0)}
Mapping Diagram: It is a function if the x-value points to only one y-value
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x y yx
Unit 1: Functions
Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
Graph: It is a function if it passes the vertical line test. Vertical Line Test: Draw a vertical line through the graph. If the line crosses the graph more than once it is not a function.
Unit 1: Functions
Lesson 1: Relations and Functions
Equation: Anything in the form y = mx + b is a function. Anything in the form y = ax2+ bx + c is a function. To check anything else, graph it!
Unit 1: Functions
Lesson 1: Relations and Functions
a) y = 2x + 1 b) y = 2x2 - 3 c) x2 + y2 = 4
Determine whether the following relations are functions or not
Unit 1: Functions
Lesson 1: Relations and Functions
Domain: The set of all the input values that are defined for a function. (Formerly referred to as the x-values or the independent variable.) Written from smallest to largest number.Range: The set of all the output values for the function. Can be determined by subbing in the values from the domain. (Formerly referred to as the y-values or the dependent variable.) Also written from smallest to largest number.
Unit 1: Functions
Lesson 1: Relations and Functions
Unit 1: Functions
Lesson 1: Relations and Functions
Example: Write the domain and range for this function using set notation.
x y1 53 67 82 8
Unit 1: Functions
Lesson 1: Relations and Functions
Example: Write the domain and range for this function using set notation.
f = {(1,-4), (2,5), (8, 9), (0, 6)}
Unit 1: Functions
Lesson 1: Relations and Functions
Example: Write the domain and range for this function using set notation.
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x y
Unit 1: Functions
Lesson 1: Relations and Functions
Example: Write the domain and range for this function using set notation.
Unit 1: Functions
Lesson 1: Relations and Functions
Practice
Level 4: pg. 10-12 # 1 – 12, 14
Level 3: pg. 10-12 # 1 – 10, 14
Level 2: Pg. 10-12 #1-7, 14
Level 1: Pg. 10-12 #1 -3, 14