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.

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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