Differentiating between relations and functions Lesson 25 Differentiating between relations and functions

Domain, range, and relation The domain is the set of possible values for the independent variable (input values) of a set of ordered pairs. The range is the set of values for the dependent variable (output values) of a set of ordered pairs. A relation is a set of ordered pairs where each number in the domain is matched to one or more numbers in the range. Relations can also be represented using set notation, diagrams, tables , or equations.

Determining the domain and range of a relation Give the domain and range of the following: (2,6), (2,10), (8,6) , (5,1) , (4,6), (3,9) Domain = 2,3,4,5,8 Range = 1,6, 9 , 10 2 1 3 6 9 4 10 5 8

function A function is a mathematical relationship pairing each value in the domain with EXACTLY one value in the range.

Identifying functions Determine if (3,3), (10,1), (0,3) , (8,9), (4,4), (10,2) is a function. 10 in the domain is matched up with 1 and 2 in the range, so this is NOT a function. Is y = 1/2 x-1 a function ? Make a table of values x -4 2 6 8 y -1 0 2 3 YES, this is a function

Vertical line test A graph on a coordinate plane represents a function if any vertical line intersects the graph in exactly one point

Identifying a graph as a function Graph points: (-6,-4) (0,-1) (2,0) (5, 3/2) (7, 5/2). Draw the line that connects them. Then do vertical line test - no matter what vertical line is drawn, the graph is intersected at only one point by each line

Writing a function The dependent variable is a function of the independent variable so "y is a function of x" Write x + 2y = 5 in function form Solve for y 2y = -x +5 y = -1 x + 5 2 2 f(x) = -1 x + 5 Read f(x) as "f of x"

Practice Write x-3y = 4 in function form

Lesson 30 graphing functions A linear equation is an equation whose graph is a line. You can use a table of ordered pairs to graph an equation. To determine if the graph is a function, use the vertical line test. A linear function is a function whose graph is a line A linear function can be written in the form f(x) = mx + b, where m and b are real numbers

Using tables to graph functions y= x graph and decide whether it is a function 1) make a table of values 2) graph the ordered pairs 3) do vertical line test y = x2 graph and decide whether it is a function

Matching a graph to a table Look at the ordered pairs and find which graph contains each one of them (see page 180 in text book- example 3)

Matching an equation to a graph Find 3 ordered pairs for each equation. Check to see which graph includes the ordered pairs See page 180-181 in text book - example 3

Identifying domain and range Look at examples in text book p. 181- example 4 and lesson practice f and g p. 183

Lab 2 creating a table You can use your graphing calculator to quickly make a table of values. To make a table for the equation y=3x+5, when x= 15,45,75,105,135: Press Y= key Then press 3 x + 5 to open table setup press 2nd window Tblstart = 15 tbl = 30 Press ENTER

Use your calculator Make a table for y = 2x-2 for x = 2,5,8,11