2. Aim: Functions/Relations Course: Alg. 2 & Trig. Aim: What is the difference between and relation and a function? Do Now: Fill in the empty spaces of the table below and determine the rule that governs your decision. x013 y01416 2 9 4 y = x 2

3. Aim: Functions/Relations Course: Alg. 2 & Trig. Relations {(0, 0), (1, 1), (2, 4), (3, 9), (4, 16)} Set of ordered pairs another way of writing table results? A relation is a set of ordered pairs. Height (in.)Player 79Hector 84Shaquille 81Allan 73Charlie 79Jerome {(79, Hector), (84, Shaquille), (81, Allan), (73, Charlie), (79, Jerome)} Relations are everywhere: basketball team

4. Aim: Functions/Relations Course: Alg. 2 & Trig. Mapping diagram Relations- Domain & Range {(0, 0), (1, 1), (2, 4), (3, 9), (4, 16)} A relation is a set of ordered pairs. {(79, Hector), (84, Shaquille), (81, Allan), (73, Charlie), (79, Jerome)} 73 81 79 84 Charlie Hector Jerome Allan Shaquille 0123401234 0 1 4 9 16 Domain - the set of all first elements of the ordered pairs Range - the set of all second elements of the ordered pairs

5. Aim: Functions/Relations Course: Alg. 2 & Trig. Rule for this relation = Relations - Domain & Range A relation is a set of ordered pairs. {(x,y)|y = x 2 and x  real numbers When the number of ordered pairs in a relation is infinite, we apply a rule to the relationship. Graphically {(0, 0), (1, 1), (2, 4), (3, 9), (4, 16)} (1,1) (2,4) (3,9) (4,16) in coordinate geometry x – domain; y – range If domain is not specified - assume all real numbers (0, 0) y = x 2

6. Aim: Functions/Relations Course: Alg. 2 & Trig. Function 73 81 79 84 Charlie Hector Jerome Allan Shaquille Our Basketball Team Charlie Hector Jerome Allan Shaquille 73 81 79 84 Relation a set of ordered pairs Function is a relation in which each element of domain corresponds to one and only one element in the range

7. Aim: Functions/Relations Course: Alg. 2 & Trig. Mathematical Function Determine if the tables below are functions xyxy 11-2 12-30 13063 207-21 yes, there is only 1 y-value assigned to each x-value no, the x-value, -2, has two y-values assigned to it, -1 and 1

8. Aim: Functions/Relations Course: Alg. 2 & Trig. Functions in Real Life The average life span of United States is a function of the value of the currency. For instance, a $1 bill has an average life span of 1.5 years, a $5 bill have an average life span of 2 years, etc. Value, x$1$5$10$20$50$100 Life Span, y 1.5 yrs 2 yrs 3 yrs 4 yrs5 yrs9 yrs For every value of x (input) there is assigned one, and only one, value of y (output).

9. Aim: Functions/Relations Course: Alg. 2 & Trig. independent variable input values dependent variable output values Function Rule A equation that describes a function. y = 3x + 4linear function y = 4constant function y = x 2 + 4x + 4quadratic function y = | ax + b |absolute value function y = [x]step function in coordinate geometry x – domain; y – range

10. Aim: Functions/Relations Course: Alg. 2 & Trig. (0, 0) (1,1) (2,4) (3,9) (4,16) Function - Coordinate Geometry Function is a relation in which each element of domain corresponds to one and only one element in the range Function every element x of domain corresponds to one and only one element y in the range Vertical line test If each vertical line drawn through the relation intersects the graph at one and only point, then the relation is a function. is a function y = x 2

11. Aim: Functions/Relations Course: Alg. 2 & Trig. Function - Model Problems Vertical line test Determine if the graphs represent functions NO YES

12. Aim: Functions/Relations Course: Alg. 2 & Trig. Function - Model Problems Does the mapping diagram represent a function? Explain. A. 12 435 3 6 4 5 7 input output No, the input 1 results in two output values instead of just one as required of a function. B. 12 435 3 6 4 5 7 input output Yes, all imputs generate one and only one output value as required of a function.

13. Aim: Functions/Relations Course: Alg. 2 & Trig. Evaluate for x = –2 Evaluating a Function Rule y = 3x + 4 y = 4 y = x 2 + 4x + 4 y = | 2x – 6 | y = 3(–2) + 4 = –2 y = 4 y = (–2) 2 + 4(–2) + 4 = 0 y = | 2(–2) – 6 | = 10