1. Functions

2. Function Notation f(x) is a fancy way of saying ____. Why use function notation?

3. How can we tell if a relation between two variables represents a function? Every value for _____ must yield _______ _____ value for _____. Does the relation (0, 1), (1, 2), (2, 2), (3, 4) represent a function? Does the relation (0, 1), (0, 2), (1, 3), (2, 4) represent a function?

4. Checking graphically? Vertical Line Test: If you can draw a vertical line through any part of the graph and it hits at _____ _____ ____ place, the graph does not represent a function. Is a function?

5. Domain The domain of a function tells us what values can be entered for _____ to give a real number solution. Types of problems that cause a restriction on the domain: –Fractions –Square Roots –Real World Problems

6. Examples (Give domain of each function) 1) 2) 3) The price for a prom ticket is $60 and the cost for running the prom is $8,000. Write a function that relates the number of tickets sold, x, to the profit P(x) and give the domain.

7. Range The range of a function tells us all of the possible real solutions that we could get for ____. Types of Problems that cause restrictions on the range: –Fractions –Square Roots –Absolute Values & Even powered polynomials –Real World Problems

8. Examples (Give the range for each function) 1) 2) 3) 4) Find the range of the Prom problem

9. Zeros of a Function The zeros of a function are the values for x that make the value of the function (or “y”) equal to zero Zeros are also called: –Roots –X-intercepts –Solutions

10. Examples (Find the zeros of each function) 1) 2)

11. Find the domain, range, and zeros of each of the following functions 1) 2) 3) 4)

12. Practice Pg. 122 ( 1 – 15 odd)

13. Step Functions A cell phone company charges $20/month for service and $1 for every minute or fraction of a minute over the plan. –What is the lowest payment you could have with this company? –What would your monthly cost be if you talked for 4.5 minutes over the plan?

14. Piecewise Functions Sketch the graph for Then, give the domain, range, and zeros.

15. Piecewise Functions (Ex2) Graph and give the domain, range and zeros

16. Ex3) Graph and give the domain, range and zeros