Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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 -1 1 3 9 -6 11 This is a function since each element of the domain (x) corresponds to only one element in the range (y). It doesn’t matter if two elements of the domain are paired with the same element in the range. Identify Functions x y -3 6 2 5 3 1 2 4 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 = 7 + 4 = 11 simplify 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. 2 • f(n) = n – 3n + 4 f(n) = 2 n – 3n + 4 • f(4) = 42 – 3(4) + 4 = 16 – 12 + 4 =4+4=8