1. 8-1 Relations and Functions

2. RELATIONS Relation: A set of ordered pairs. Domain: The x values of the ordered pairs. Also known as the input value. Range: The y values of the ordered pairs. Also known as the output value. Relations can be represented by ordered pairs in a table, a coordinate graph, or a mapping.

3. {(4,1), (2,4), (-4,1), (2,-5), (0,-3), (-3,-3)} A relation: Table x y 4 1 2 4 -4 1 2 -5 0 -3 List the x- coordinate in the first column and the y-coordinate in the second column. x y Graph Mapping -4 -3 0 2 4 -5 -3 1 4 xy

4. Identify the domain and range Remember, the domain is the x values or the input The range is the y values or the output They should be listed in increasing order with brackets around them You should NOT list the repeated values again.

5. Find domain and range x y 4 1 2 4 -4 1 2 -5 0 -3 Domain: 4, 2, -4, 2, 0, -3 Put in order… Range: 1, 4, 1, -5, -3, -3 Put in order… Range Range: {-5,-3,1,4} Domain Domain: {-4,-3,0,2,4}

6. Period Grade 1 4 2 3 3 3 4 4 5 4 6 2 Tri 1 Report Card functions Some relations are functions. function In a function, each member of the domain is paired with exactly one member of the range. domain range 1 4 2 3 3 3 4 4 5 4 6 2 A=4 B=3 C=2 D=1 F=0 Alphabetical order: domain listed before range!

7. domain range 1 2 2 4 1 3 4 8 5 10 function Is the relation a function? Explain. {(1,2), (2,4), (1,3), (4,8), (5,10)} function No, it is not a function, because the domain for 1 has two ranges.

8. Remember: the domain is given before the range! domain range 1 2 2 4 1 2 4 8 5 10 function Is the relation a function? Explain. Presenting the data in a table may make it easier to tell if the relation is a function. {(1,2), (2,4), (1,2), (4,8), (5,10)} function Yes, it is a function, because for each domain there is only one range.

9. domain range 2 1 4 2 6 3 2 1 4 2 function Example 2 Is the relation a function? Explain. function Yes, it is a function, because for each domain there is only one range.

10. domain range 2 2 4 1 6 0 2 2 4 function Example 3 Is the relation a function? Explain. function No, it is not a function, because domain 4 has different ranges.

11. A vertical line test is used to determine whether a graph represents a function. A graph is a function if any vertical line intersects the graph at no more than one point. x (domain) y (range) The graph is a function.

12. You can use your pencil to check. Keep your pencil straight to represent a vertical line and pass it across the graph. If it touches the graph at more than one point, the graph is not a function. x (domain) y (range)

13. A vertical line test is used to determine whether a graph represents a function. A graph is a function if any vertical line intersects the graph at no more than one point. x (domain) y (range) The graph is NOT a function.

14. A vertical line test is used to determine whether a graph represents a function. A graph is a function if any vertical line intersects the graph at no more than one point. x (domain) y (range) The graph is NOT a function.

15. A vertical line test is used to determine whether a graph represents a function. A graph is a function if any vertical line intersects the graph at no more than one point. x (domain) y (range) The graph is a function.

16. A vertical line test is used to determine whether a graph represents a function. A graph is a function if any vertical line intersects the graph at no more than one point. x (domain) y (range) The graph is NOT a function.