1.4 FUNCTIONS!!! CALCULUS 9/10/14 -9/11/14
WARM-UP Write a general equation to represent the total cost, C, in a business problem. How is it different from the Revenue equation? Your calculator gives you an error of invaliddim or you can’t see your graph, what are some things we need to check to make it work?
1.4 FUNCTIONS Function – a relationship between two variables such that each value of the independent variable there corresponds exactly one value of the dependent variable Domain – set of all values of the independent variable for which the graph is defined Range- the set of all values taken on by the dependent variable
IS IT A FUNCTION? – TWO WAYS TO DECIDE Isolate the dependent variable on the left side (“y = ___”) x+y = 1 Is y is a function of x? y = x + 1 Vertical Line Test
WHICH OF THE FOLLOWING EQUATIONS DEFINE Y AS A FUNCTION OF X?
DOMAIN AND RANGE (WILL COME UP A LOT)
ONE – TO – ONE FUNCTIONS Each value of the dependent variable in the range corresponds with exactly one value of the independent variable Horizontal Line Test
EVALUATING FUNCTIONS
EVALUATING FUNCTIONS – DIFFERENCE QUOTIENT
COMBINATIONS OF FUNCTIONS f(x) + g(x) f(x) – g(x) f(x)g(x) f(x)/g(x)
COMPOSITE FUNCTION
INVERSE FUNCTIONS
ARE THEY INVERSES?
FIND THE INVERSE (FIND DOMAIN AND RANGE OF EACH)
EXAMPLE
FIND THE INVERSE