Lesson 1: Relations and Functions Unit 1: Functions Lesson 1: Relations and Functions Learning Goals: I can determine if a relation is a function

Lesson 1: Relations and Functions 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. A relation is a connection (or relationship) between two sets of numbers, such as height vs. time or cost vs. weight The Dependent Variable is: The Independent Variable is:

Lesson 1: Relations and Functions 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.

Lesson 1: Relations and Functions Unit 1: Functions Lesson 1: Relations and Functions   These examples represent function notation and are read as, “ f of x”, or “f at x”.

Lesson 1: Relations and Functions 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)

Lesson 1: Relations and Functions 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.

Lesson 1: Relations and Functions Unit 1: Functions Lesson 1: Relations and Functions Example: INPUT OUTPUT INPUT OUTPUT Camary Rav 4 Yaris Prius Camary Venza Rav 4 Sienna Yaris Corolla Prius Toyota Toyota

Lesson 1: Relations and Functions Unit 1: Functions Lesson 1: Relations and Functions A function can be represented by: A Table of Values A Set of Ordered Pairs A Mapping Diagram A Graph An Equation

Lesson 1: Relations and Functions 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 2 1 x y 1 5 3 6 7 8 2

Lesson 1: Relations and Functions 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)}

Lesson 1: Relations and Functions Unit 1: Functions Lesson 1: Relations and Functions Mapping Diagram: It is a function if the x-value points to only one y-value y 1 4 7 10 11 8 9 x y x 1 -1 1 2 3 4

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.

Lesson 1: Relations and Functions 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!

Lesson 1: Relations and Functions Unit 1: Functions Lesson 1: Relations and Functions Determine whether the following relations are functions or not a) y = 2x + 1 b) y = 2x2 - 3 c) x2 + y2 = 4

Lesson 1: Relations and Functions 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.

Lesson 1: Relations and Functions Unit 1: Functions Lesson 1: Relations and 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 y 1 5 3 6 7 8 2

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. f = {(1,-4), (2,5), (8, 9), (0, 6)}

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. 1 4 7 10 11 8 9 x y

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.

Lesson 1: Relations and Functions 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