Functions Introduction

43210 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will be able to understand the concept of a function. - Correctly use function terminology (domain, range, f(x)). - Determine if a relationship given in a table, graph, or words depicts a function. With help from the teacher, the student has partial success with function terminology, function notation and determining if a relation table or graph depict a function. Even with help, the student has no success understanding the concept of a function. Learning Goal for Focus 3 (HS.A-CED.A.1, HS.F-IF.A.1 & 2, HS.F-IF.B.4 & 5): The student will understand the concept of a function and use of function notation.

Definition #1 Relation

Definition #2 Function

How to determine if a relation is a function:  Analyze the x-values given in ordered pairs or in a table.  If an x repeats with a different y-value, then it is NOT a function.  Practice: Is this relation a function? 1. H = {(2, 5), (3, 9), (-4, 10), (6, -6), (-7, 5)} 2. M = {(3, 7), (-8, 2), (-1, 0), (3, 8), (2, 6)} YES! NO!

How to determine if a graph is a function:  Vertical Line Test  If you draw a vertical line anywhere on the graph and it goes through only one point = FUNCTION  If you draw a vertical line anywhere on the graph and it goes through more than one point = NOT a Function.  Practice: Is this graph a function? x y x y NO! YES! NO!

Definition #3 Domain  Domain: All of the input values, x-values.  These are referred to as independent values. Definition #4 Range  Range: All of the output values, y-values.  These are referred to as dependent values.

State the domain and range of the following relations:  (grade, student name)  Set A = {(A, Frankie), (C, Denise), (B, Brady), (A, Julietta), (D, Bob), (B, Evelyn)}  Domain: {A, C, B, D}  Range: {Frankie, Denise, Brady, Julietta, Bob, Evelyn}  Is this a function?  (x, y)  Set W = {(3, 4), (5, 9), (-6, 4), (8, 12)  Domain: {3, 5, -6, 8}  Range: {4, 9, 12}  Is this a function? NO! YES!

State the domain and range of the following graphs:  Domain: {-1, 1, 3, 4, 6}  Range: {1, 4, -3, 3}  Is it a function? YES!  Domain: {All real numbers}  Range: {y ≥ -4}  Is it a function? YES!  Domain: {2}  Range: {All real numbers}  Is it a function? NO!

 Play 2 nd video on the page.