Functions 4-6 I can determine whether a relation is a function and find function values. S. Calahan 2008

What is a function? A function is a relation in which each element of the domain is paired with exactly one element of the range.

Identify Functions x y -4 9 This is a function since each element of the domain (x) corresponds to only one 1 11 element in the range (y). 3 It doesn’t matter if two elements of the domain are paired with the same element in the range.

Identify Functions x y The table represents a relation that is not a function because there are two of the same elements in the domain (x).

Vertical Line Test Use the vertical line test to determine if a graph represents a function. If a vertical line can be drawn so that it intersects the graph no more than once the graph is a function. If a vertical line can be drawn so that it intersects the graph at two or more points the graph is not a function.

Vertical Line Test Not a function, because it crosses twice

Vertical line test This is a function because it crosses only once no matter where you draw the line.

Function Notation Equations that are functions can be written in function notation form Example: y = 3x – 8 equation f(x) = 3x – 8 function notation

Function Values f(x) = 2x + 5 for f(-2) f(-2) = 2(-2) + 5 = 1 Substitute the value inside the ( ) in for the variable inside the ( ).

f(x) = 2x + 5 f(1) + 4 = [2(1) + 5] + 4 Substitute the 1 in for the x then add the 4 at the end of the expression. = [2 + 5] + 4 simplify = = 11 add

Nonlinear Functions A function that is nonlinear can be solved the same way as a linear function. Nonlinear functions can have an exponent on one of the variables. f(n) = n 2 – 3n + 4

f(4) = 4 2 – 3(4) + 4 = 16 – = = 8