8th Grade Math Presented by Mr. Laws x Domain (x) Range (y) 2 5 11 14 -3 3 4 Function Rule 8th Grade Math Presented by Mr. Laws

CCSS Standard 8.F.1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Essential Question How do I explain that a function is rule that assigns each input exactly one output?

What is a Function? A function is a relationship that corresponds between a input value (x), and output value (y). To be a function each input (x) can have only one and only one output (y). Functions can be represented by order pairs, mapping diagram, function table , or graph.

The Function Rule Input (x) Output (y) 1 2 4 6 8 Input (x) Output (y) A function input (x) can only relate to one output (y). Input (x) Output (y) 1 2 4 6 8 Input (x) Output (y) 1 2 4 3 6 8 This is not a function. Input (x) value 2 has two different outputs (y) value 4 and 8. This is a function!

Functions (Order Pairs) To be a function , the x value cannot be repeated in order pairs. Example #1: {(1,2), (3, 4), (5, 6), (7, 9), (8, 0), (9, 1)} This set of order pairs is a function! Example #2: {(1,2), (3, 4), (5, 6), (7, 8), (1, 0), (9, 1)} This set of order pairs is not a function! Why?

Functions (Mapping Diagram) A mapping diagram helps illustrate or map the corresponding relationship between the domain (x), and the range (y). Domain (x) Range (y) Mapping Order pairs: { (-2,3), (-1, 5), (0,7), (1, 9), (2, 11)}. 3 5 7 9 11 -2 -1 1 2 Domain (x) values: { -2, -1, 0, 1, 2} Range (y) values: { 3, 5, 7, 9, 11}

Functions (Mapping Diagram) Create a mapping diagram for the following order pairs: { (-3, 5), (2, 2), (3, 5), (4, 10)} Domain (x) Range (y) 2 5 10 -3 3 4 Is this a Function? YES! – the domain does not repeat

Functions (Mapping Diagram) Create a mapping diagram for the following order pairs: { (2,6), (4,10), (4, 13), (5,15), (6, 12)} Domain (x) Range (y) 6 10 13 12 15 2 4 5 Is this a Function? NO! – the domain x-value repeats

Function Tables Functions can be organize by Vertical or horizontial tables, which the domain (x) and range (y) variable is shown. Sales Price vs. Orig. Price Original Price (x) $5 $10 $15 $20 $25 Sale Price (y) $1 $2 $3 $4 X Y 1 2 4 3 6 8 Horizontal Function Table Can you explain the relationship of (x) and (y)? What will the sale price be if the original price was $45? Vertical Function Table

Function (Graph) A function graph is a set of order pairs (x,y) plotted on a coordinate plane. You can identify whether a graph is a function by using the vertical line test. y x y x Vertical Line Test – cross the line once, it is a function. Vertical Line Test – cross the line twice it is not a function.

Function (Graph) A function graph is a set of order pairs (x,y) plotted on a coordinate plane. You can identify whether a graph is a function by using the vertical line test. y x y x Vertical Line Test – cross through one plot, it is a function. Vertical Line Test – cross through two or more it is not a function.

Summary Can you answer the essential question? Do you have any questions on what you have learned? Will you be able to write a summary based on the lesson?