Class Opener:

1. Class Opener: • You have 5 minutes to come up with the largest prime number you possible can.

2. Homework Review Pg. 11 – 13 #10, 55, 72

3. A function: • A function f from set A to set B is a relation that assigns to each element x in the set A exactly one element y in the set B. The set A is the domain of the function f, and the set B contains the range of the function.

4. Characteristics of a Function • Each element of A much be matched with an element of B • Some elements of B may not be matched with any element of A • Two or more elements of A may be matched with the same element of B • An elementof A cannot be matched with two different elements of B

5. Example: Determine which of the equations represents y as a function of X?

6. Example: • Determine if the following equations are functions:

7. Review of Function Notation • f(x) = range • x = domain

8. Example: • Evaluate the Function for g(2), g(t), and g(x+2)

9. Example: • Evaluate the function at each specified value of the independent variable and simplify. • h(2) b) h(1.5) c)h(x+2)

10. Piecewise Function • A piecewise –defined function is a function that is defined by two or more equations over a specified domain. The absolute value function given by f(x) = x can be written as a piecewise – defined function.

11. Example • Evaluate the function when x = -1 and x = 0

12. Example: • Evaluate the function at each specified value of the independent variable and simplify • f(-1) b) f(0) c) f(2)

13. Implied Domain • The domain of a function can be described explicitly or it can be implied by the expression used to define the function. The IMPLIED DOMAIN is the set of all real numbers for which the expression is defined. For Example:

14. Radical Functions • Radical functions arise from the use of rational exponents. The most common radical function is the square root function.

15. Class Opener: • A rectangular package to be sent by the U.S. Postal Service can have a maximum combined length and girth(perimeter of cross section) of 108 inches. • Write the volume V of the package as a function of x. What is the domain of the function? • Use a graphing utility to graph the function. Make sure to have the appropriate window. • What dimensions will maximize the volume of the package?

16. Example: • Find the domain of each function: • Volume of a Sphere:

17. Example: • Find the domain of the given function:

18. Put Technology to Work • Using the graphing calculator find the domain and range of the following function:

19. Example: • Use a graphing calculator to find the domain and range of the following functions.

20. Real World Connections The number N (in thousands) of employees in the cellular communications industry in the U.S. increase in a linear pattern from 1998 – 2001. In 2002, the number dropped, then continued to increase through 2004 in a different linear pattern . These two patters can be approximated by the function: Where t = years, and 8 = 1998. Use this function to approximate the number of employees for each ear from 1998 to 2004 .

21. Physics Connection A baseball is hit at a point 3 feet above the ground at a velocity of 100 ft/s and at an angle of 45 degrees. The path of the baseball is given by the function: Will the baseball clear a 10 foot fence located 300 feet from home plate? Left Side of Room Work it by Hand Right Side of Room work it graphically on a calculator

22. Calculus Connection • One of the basic definitions for calculus employs the ratio: This is known as the difference quotient.

23. Evaluating with Difference Quotient For find the difference Quotient.

24. Find the Difference Quotient

25. assignment • Pg. 11 – 15 • Exs. 12 – 32 even, 39 – 46, 52 – 62 even, 68 – 74 even, 79 – 82, 85 – 87, 91 – 102, 113 – 116