1. 1.4 FUNCTIONS!!! CALCULUS 9/10/14 -9/11/14

2. 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?

3. 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

4. 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

5. WHICH OF THE FOLLOWING EQUATIONS DEFINE Y AS A FUNCTION OF X?

6. DOMAIN AND RANGE (WILL COME UP A LOT)

7. 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

8. EVALUATING FUNCTIONS

9. EVALUATING FUNCTIONS – DIFFERENCE QUOTIENT

10. COMBINATIONS OF FUNCTIONS  f(x) + g(x)  f(x) – g(x)  f(x)g(x)  f(x)/g(x)

11. COMPOSITE FUNCTION

12. INVERSE FUNCTIONS

14. ARE THEY INVERSES?

15. FIND THE INVERSE (FIND DOMAIN AND RANGE OF EACH)

16. EXAMPLE

17. FIND THE INVERSE