3.2 Understanding Relations and Functions

Relations can be represented as A relation is a set of ordered pairs (x, y) where x is the input value and y is the output value. x 1 5 8 4 y a b c d Relations can be represented as ordered pairs, mappings, graphs or tables.

Domain: all possible inputs of a relation Range: all possible outputs of a relation Domain: {4, -2, 5, 0} Range: {5, 1, 6, 2}

Function – A pairing of inputs with outputs such that each input has only one output 5 -8 4 -9 3.5 14 -3

Explain…

State the domain and range of the function. Domain-The set of all inputs of a function (independent) Range-The set of all outputs of a function (dependent) State the domain and range of the function. Input 5 -8 4 Output -9 3.5 14 -3

Is this relation a function? Detroit Lions Green Bay Packers Chicago Bears Minneapolis Vikings New York Jets Giants

Explain whether the situation always represents a function. 1. A teacher makes a list of email addresses, y, for the parents of all of her students, x. 2. A student inputs the first names, x, of all her friends with their telephone numbers, y. 3. The cost of apples, y, depends on the number of apples, x.

State the dependent and the independent value. 1. A teacher makes a list of email addresses, y, for the parents of all of her students, x. 2. A student inputs the first names, x, of all her friends with their telephone numbers, y. 3. The cost of apples, y, depends on the number of apples, x.

Given the table below… Is the pairing a function? Write a rule. Input 1 2 3 8 Output -2 -1 6 Is the pairing a function? Write a rule.

Given the function: y = 2x - 9 Identify the range if the domain is {-4, 0, 1, 11}

Gus is teaching guitar lessons. What is a reasonable domain for cost per lesson? List 3 unreasonable domain values.

Represent Functions as Graphs Make an input-output table for y = 2x – 3 with domain {-2, 0, 6} Graph the function.

Write a rule for the function. Find a value for y so that (2.5, y) is on the graph.

Is the relation a function? Input 2 6 7 Output 9 -2 Input 9 -2 6 Output 2 7

Does this graph represent a function? Explain.

Homework Page 112 #12-14 Page 120 #1, 2, 6-9, 12-15, 17-25 (odd)