Objective SWBAT define and identify functions SWBAT will identify and plot points in a coordinate plane

FUNCTION- DOMAIN containing numbers called INPUTS The horizontal axis (x-axis) is labeled with the input variable. represents a relationship between one variable to another. Consists of the following: DOMAIN containing numbers called INPUTS RANGE containing numbers called OUTPUTS The vertical axis (y-axis) is labeled with the output variable. Each input must be paired with only ONE output

“To Be or Not To Be” a FUNCTION 1 2 Output 12 9 6 3 Input 3 2 1 Output 7 4 Input FUNCTION NOT A FUNCTION 3 6 9 12 1 2 2 1 2 4 7 0 1 2 3 The pairing is a function because each input is paired with exactly one output. The pairing is not a function because each input is not paired with exactly one output.

“To Be or Not To Be” a FUNCTION 3 1 7 5 Output Input 1 Output 8 6 4 2 Input FUNCTION NOT A FUNCTION 3 5 5 1 2 3 2 4 6 8 0 1 0 1 The pairing is not a function because each input is not paired with exactly one output. The pairing is a function because each input is paired with exactly one output.

Chapter 4 “Graphing Linear Equations and Functions” (4.1) Plot Points in a Coordinate Plane (4.2) Graph Linear Equations (4.3) Graph Using Intercepts (4.4) Find Slope and Rate of Change (4.5) Graph Using Slope-Intercept Form (4.7) Graph Linear Functions

Coordinate Plane y-axis Quadrant II (-,+) Quadrant I (+,+) Origin (0,0) x-axis Quadrant III (-,-) Quadrant IV (+,-)

Plotting Points (2,4) (-3,4) (2,-3) (-6,-4) y-axis x-axis ordered pair (input, output) y-axis (-3,4) 5 C 4 A 3 (2,-3) 2 x – coordinate (input) 1 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 y – coordinate (output) (-6,-4) -2 -3 B D -4 -5 x-axis

The range of the function is 8, 6, 4, 2, 0. Graphing a Function Graph the function y = 4 – 2x with the domain -2, -1, 0, 1, and 2. Then identify the range of the function. y-axis 10 (-2,8) 8 x y (-1,6) 6 -2 8 4 (0,4) (1,2) -1 6 2 4 -12 -10 -8 -6 -4 -2 2 4 6 8 10 12 x-axis (2,0) 1 2 -2 2 -4 -6 The range of the function is 8, 6, 4, 2, 0. -8 -10

Graph a Function Graph the function y = 2x – 1 with domain – 2, – 1, 0, 1, and 2. Then identify the range of the function. SOLUTION STEP 2 STEP 3 STEP 1 List the ordered pairs: (– 2, – 5),(– 1, – 3), (0, – 1), (1, 1), (2, 3).Then graph the function. Identify the range. The range consists of the y-values from the table: – 5, – 3, – 1, 1, and 3. Make a table by substituting the domain values into the function.

Graph a Table Years before or since 1920 – 12 – 8 – 4 4 8 12 In 1920 the ratification of the 19th amendment to the United States Constitution gave women the right to vote. The table shows the number (to the nearest million) of votes cast in presidential elections both before and since women were able to vote. Years before or since 1920 – 12 – 8 – 4 4 8 12 Votes (millions) 15 19 27 29 37 40 Explain how you know that the table represents a function. a. Graph the function represented by the table. b.

Graph a function SOLUTION The table represents a function because each input has exactly one output. a. To graph the function, let x be the number of years before or since 1920. Let y be the number of votes cast (in millions). b.