1. 1-6 and 1- 7: Relations and Functions Objectives: Understand, draw, and determine if a relation is a function. Graph & write linear equations, determine domain and range.

2. Relations & Functions Relation: a set of ordered pairs Domain: the set of x-coordinates Range: the set of y-coordinates When writing the domain and range, do not repeat values.

3. Relations and Functions Given the relation: {(2, -6), (1, 4), (2, 4), (0,0), (1, -6), (3, 0)} State the domain: D: {0,1, 2, 3} State the range: R: {-6, 0, 4}

4. Relations and Functions Another way to represent a relation is to use a mapping diagram. Create two ovals with the domain on the left and the range on the right. Elements are not repeated. Connect elements of the domain with the corresponding elements in the range by drawing an arrow

5. Mapping {(2, -6), (1, 4), (2, 4), (0, 0), (1, -6), (3, 0)} 21032103 -6 4 0

6. Mapping The elements of the domain are called inputs, and the elements of the range are called outputs.

7. Relations and Functions Sometimes a relation is represented by a table. {(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)}

8. Relations and Functions Another way to represent a relation is to draw its graph. {(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)}

9. Functions A function is a relation in which the members of the domain (x-values) DO NOT repeat. So, for every x-value there is only one y-value that corresponds to it. y-values can be repeated.

10. Functions When no two elements of the domain are mapped to the same elements of the range, it is called one-to-one mapping.

11. Do the ordered pairs represent a function? {(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)} No, 3 is repeated in the domain. {(4, 1), (5, 2), (8, 2), (9, 8)} Yes, no x-coordinate is repeated.

12. Graphs of a Function A horizontal line is a constant function. A linear function is a function whose graph is a line or part of a line.

13. Graphs of a Function If a vertical line is passed over the graph and it intersects the graph in exactly one point, the graph represents a function.

14. x y x y Is the graph a function? Why/not?

15. x y x y

16. Function Notation When we know that a relation is a function, the “y” in the equation can be replaced with f(x). f(x) is simply a notation to designate a function. It is pronounced ‘f’ of ‘x’. The ‘f’ names the function, the ‘x’ tells the variable that is being used.

17. Value of a Function Since the equation y = x - 2 represents a function, we can also write it as f(x) = x - 2. Find f(4): f(4) = 4 - 2 f(4) = 2

18. Value of a Function If g(s) = 2s + 3, find g(-2). g(-2) = 2(-2) + 3 =-4 + 3 = -1 g(-2) = -1