Function Notation. 43210 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts.

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Function Notation

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.

Function: Is a correspondence between two sets, X and Y, in which each element of X is matched to one and only one element of Y. The set X is called the domain of the function.  The notation f: X → Y is used to name that function that describes both X and Y.  If x is an element in the domain X of a function f: X → Y, then x is matched to an element of Y called f(x).  Examples:  f: {students in 8 th grade} → {their math teacher}  The domain of this function is students in 8 th grade.  Each student of the domain is matched to a math teacher at the school.  Suppose f(David) = Jensen. What does that mean?  This means that David has Jensen as a math teacher.  Suppose f(Julio) = Holdcraft. What does that mean?  This means Julio has Holdcraft as a math teacher.

Another example:  Let X = {1, 2, 3, 4} and Y = {5, 6, 7, 8}  f: X → Y  f = {(1, 7), (2, 5), (3, 6), (4, 8)}  What is f(2) ?  f(2) = 5 since 2 is matched to 5.  What is f(4) ?  f(4) = 8 since 8 is matched to 4.  If f(x) = 7, then what might x be?  If f(x) = 7, then x = 1

Function Notation  This is a way of writing a function. It is a precise way of giving information about the function without writing a long explanation.  The most popular way to write a function is f(x).  This is read “f of x”  (This is NOT multiplying f times x.)  Example:  f(x) = 2x + 4 InputOutput {

How to use f(x)…  f(x) = 2x + 7, find f(5).  This means to substitute 5 in where you see x.  f(5) = 2(5) + 7  f(5) = 17 The answer is 17.  f(x) = -3x 2 – x – 4, find f(2)  This means to substitute 2 in where you see x.  f(2) = -3(2) 2 – 2 – 4  f(2) = -18

f(x) = 6x – 3 If f(x) = 33, what does x equal?  f(x) = 33 means the answer to 6x – 3 is 33.  Substitute 33 where f(x) is.  33 = 6x – 3 Now solve for x.  36 = 6x  6 = x  The answer is that f(6) = 33.