1. Homework Questions? Welcome back to Precalculus

2. Review from Section 1.1 Summary of Equations of Lines

3. Example from Section 1.1 Find the equation of the line that passes through the points (-1,-2) and (2,6).

4. Precalculus: Functions 2015/16 Objectives: Determine whether relations between two variables represent functions Use function notation and evaluate functions Find the domains of functions Use functions to model and solve real-life problems Evaluate difference quotients

5. Definition of a Function: A function is a relation in which each element of the domain (the set of x-values, or input) is mapped to one and only one element of the range (the set of y-values, or output).

6. Illustration of a Function.

7. Slide 1.3 - 7 Diagrammatic Representation Function

8. Slide 1.3 - 8 Diagrammatic Representation Not a function

9. A Function can be represented several ways: Verbally – by a sentence that states how the input is related to the output. Numerically – in the form of a table or a list of ordered pairs. Graphically – a set of points graphed on the x-y coordinate plane. Algebraically – by an equation in two variables.

10. Example 1 Decide whether each relation represents y as a function of x. Input: x22345 Output: y13541 a)b) Not a function. 2 inputs have the same output! Function!. There are no 2 inputs have the same output.

11. Slide 1.3 - 11 Example:Identifying a function (b) y = x 2 – 2 Determine if y is a function of x. Solution (a) x = y 2 (a) If we let x = 4, then y could be either 2 or –2. So, y is not a function of x. The graph shows it fails the vertical line test.

12. Slide 1.3 - 12 (b) y = x 2 – 2 Solution (continued) Each x-value determines exactly one y-value, so y is a function of x. The graph shows it passes the vertical line test.

13. Example 2. Try this one on your own. Which of the equations represents y as a function of x? a.b. FunctionNot a function

14. Example 3: Evaluating functions. Let g(2)= g(t) = g(x+2)=

15. You Try. Evaluate the following function for the specified values. Let h(0)= h(2)= h(x+1)=

16. Example 4. Evaluating a piecewise function.

17. You try.

18. Understanding Domain Domain refers to the set of all possible input values for which a function is defined. Can you think of a function that might be undefined for particular values?

19. Can you evaluate this function at x=3? Because division by zero is undefined, all values that result in division by zero are excluded from the domain.

20. Can you solve this equation? Radicands of even roots must be positive expressions. Remember this to find the domain of functions involving even roots. Why not? So is undefined.

21. Example 5 : Find the domain of each function g(x): {(-3,0),(-1,4),(0,2),(2,2),(4,-1)}

22. You Try: Find the domain of each function

23. Slide 1.5 - 23 Copyright © 2010 Pearson Education, Inc. The Difference Quotient The difference quotient of a function f is an expression of the form where h ≠ 0.

24. Calculating Difference Quotients Difference quotients are used in Calculus to find instantaneous rates of change.

25. Student Example Find each of the following for

26. Homework: Pg. 24 7,9, 13-23 odds, 27,33,37, 43-55 odds, 83, 85

27. Find the domain of the function and verify graphically.

28. Use your calculator to answer this: A baseball is hit at a point 3 feet above the ground at a velocity of 100 feet per second and an angle of 45 degrees. The path of the baseball is given by the function where y and x are measured in feet. Will the baseball clear a 10 foot fence located 300 feet from home plate?

29. Homework: Pg. 24 7,9, 13-23 odds, 27,33,37, 43-55 odds, 83, 85