Functions

Terms and Definitions Relation – is ANY set of inputs and their corresponding outputs They are represented by ordered pairs Examples: (4, 6), (2, 9), (8, 12), (1, 2) Function – is a special type of Relation between two sets of “variables” BIG IDEA: To be a function, each input value can have ONLY ONE output value

Terms and Definitions Domain – the “input;” the set of all the “x” values in the relation Range - the “output;” the set of all the “y” values in the relation Ordered Pair - set of (x, y) Set Notation - entire set of ordered pairs { } ex: { (4, 3), (2, 6), (1, 9) }

Function Vs. Non-Function Age (years) Height (meters) (Input, Output) 18 4.25 (18, 4.25) 20 4.40 (20, 4.40) 21 5.25 (21, 5.25) 23 4.85 (23, 4.85) Function Age (years) Height (meters) (Input, Output) 18 4.25 (18, 4.25) 20 4.40 (20, 4.40) 21 5.25 (21, 5.25)

Function Vs. Non-Function Not A Function Age (years) Height (meters) (Input, Output) 18 4.25 (18, 4.25) 20 4.40 (20, 4.40) 21 5.25 (21, 5.25) 4.85 (21, 4.85) Same input – different output Not A Function Age (years) Height (meters) (Input, Output) 18 4.25 (18, 4.25) 20 4.40 (20, 4.40) 21 5.25 (21, 5.25) 3.25 (18, 3.25)

Function Relations 1 2 3 4 5 2 4 6 8 10 { } (1, 6) (2, 2) (3, 10) Domain (set of all x’s) Range (set of all y’s) { } (1, 6) (2, 2) (3, 10) (4, 8) (5, 4) This is a Function! All the x’s are used; x values are only assigned to one y.

Function Relations 1 2 3 4 5 2 4 6 8 10 { } (1, 6) (2, 6) (3, 6) Domain (set of all x’s) Range (set of all y’s) { } (1, 6) (2, 6) (3, 6) (4, 6) (5, 6) This is a Function! All the x’s are used; x values are only assigned to one y.

Function Relations 1 2 3 4 5 2 4 6 8 10 { } (1, 2) (2, 4) (2, 10) Domain (set of all x’s) Range (set of all y’s) { } (1, 2) (2, 4) (2, 10) (3, 8) (4, 6) (5, 4) This is NOT a Function! All the x’s are used; x values are assigned to more than one y

Function Relations 1 2 3 4 5 2 4 6 8 10 { } (1, 6) (2, 4) (4, 10) Domain (set of all x’s) Range (set of all y’s) { } (1, 6) (2, 4) (4, 10) (5, 8) This is NOT a Function! All the x’s are NOT used and values are assigned to one y

Function Relations 1 2 3 4 5 2 4 6 8 10 { } (1, 6) (2, 2) (3, 10) Domain (set of all x’s) Range (set of all y’s) { } (1, 6) (2, 2) (3, 10) (4, 10) (5, 4) This is a Function! All the x’s are used; x values are only assigned to one y.

Louisiana Believes Which model is NOT a function?

Function Relations X Y 5 1 7 8 3 9 This is NOT a Function! Look at the table below. Is this a function? Explain or show how you got your answer X Y 5 1 7 8 3 9 This is NOT a Function! I have a repeating “x” value with different “y” values

Function Relations A. C. B. D. Which of the following tables does NOT represent a function? X Y 3 4 1 5 2 X Y -1 1 2 A. C. B. X Y 2 8 4 6 D. X Y -3 5 -2 -1

Function Relations X Y This is a Function! Look at the table below. Is this a function? Explain or show how you got your answer X Y -2 3 -1 1 2 8 This is a Function! None of my “x’s” (inputs) repeat and they all have only one output value

Function Relations Fill in the table with values that would create a relation that is NOT a function. Then explain why it’s not a function. X Y

Function Relations Fill in the table with values that would create a relation that IS a function. Then explain why it’s not a function. X Y

Louisiana Believes Which set of ordered pairs models a function?

The Vertical Line Test Functions as ordered Pairs (inputs and outputs) can be represented in the form of a graph Vertical Line Test – can be used to determine if a graph is a function BIG IDEA - if a vertical line can be drawn and it intersects more than one point on a graph (meaning more than one output for each input), then it is NOT A FUNCTION

Functions and Graphs Is this graph a function? Explain your reasoning. Yes, this is a function. Each “x” has one output value and it can pass the vertical line test.

Functions and Graphs Is this graph a function? Explain your reasoning. Yes, this is a function. Each “x” has one output value and it can pass the vertical line test.

Functions and Graphs Is this graph a function? Explain your reasoning. No, this is NOT A FUNCTION. “x” has more than one output value and it cannot pass the vertical line test.

Functions and Graphs Which of the following is a function?

Functions and Graphs Is this graph a function? Explain your reasoning. No, this is NOT A FUNCTION. “x” has more than one output value and it cannot pass the vertical line test.

Functions and Graphs Is this graph a function? Explain your reasoning. Yes, this is a function. Each “x” has one output value and it can pass the vertical line test.

Functions and Graphs Is this graph a function? Explain your reasoning. No, this is NOT A FUNCTION. “x” has more than one output value and it cannot pass the vertical line test.

Functions and Graphs Which of the following is a function?

Functions and Graphs Make a graph that shows a function.

Functions and Graphs Make a graph that is not a function.