1. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Graphs of Functions (Section 1-3)

2. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Graph of a function f: the collection of ordered pairs (x, f(x)) such that x is in the domain of f. If you are asked to find f(x) for a specific x value…  If you have an equation, plug the number inside the parenthesis into the equation in place of x. The answer is the value you get once you have evaluated the expression.  If you have a graph, look for the point on the graph where the number inside the parenthesis is the x-coordinate. The answer is the y-coordinate at this point.

3. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Use the graph of the function to find the domain and range of f. Then find f(0). Example 1

4. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Use the graph of the function to find the domain and range of f. Then find f(0). Example 2

5. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Use the graph of the function to find the domain and range of f. Then find f(0). Example 3

6. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. To determine the domain and range algebraically:  In general, the domain, is all real numbers except if there is a number that you cannot plug into the function. (ex: a number that will result in a negative number inside an even root, or that will result in a zero in the denominator of a rational expression)  For the range, consider which y-values you can get by plugging in allowed x-values to the equation (range is easiest to determine graphically).

7. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Use a graphing utility to graph the function and estimate its domain and range. Then find the domain and range algebraically. Example 4

8. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Use a graphing utility to graph the function and estimate its domain and range. Then find the domain and range algebraically. Example 5

9. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Use a graphing utility to graph the function and estimate its domain and range. Then find the domain and range algebraically. Example 6

10. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Use the given function to answer the questions. Example 7 f(x) = x 3 – 4x (a)Determine the domain of the function (b)Find the value(s) of x such that f(x) = 0. (c)The values of x from part (b) are referred to as what graphically? (d)Find f(0), if possible. (e)The value from part (d) is referred to as what graphically? (f)What is the value of f at x = 1? What are the coordinates of the point? (g)What is the value of f at x = -1? What are the coordinates of the point? (h)The coordinates of the point on the graph of f at which x = -3, can be labeled (-3, f(-3)) or (-3, _____).

11. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Use the given function to answer the questions. Example 8 (a)Determine the domain of the function (b)Find the value(s) of x such that f(x) = 0. (c)The values of x from part (b) are referred to as what graphically? (d)Find f(0), if possible. (e)The value from part (d) is referred to as what graphically? (f)What is the value of f at x = 1? What are the coordinates of the point? (g)What is the value of f at x = -1? What are the coordinates of the point? (h)The coordinates of the point on the graph of f at which x = -3, can be labeled (-3, f(-3)) or (-3, _____).

12. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Vertical line test (pg 31): A set of points in a coordinate plane is the graph of y as a function of x if and only if no vertical line intersects the graph at more than one point.

13. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Use the Vertical Line Test to determine whether y is a function of x. Describe how you can use the graphing utility to produce the given graph. Example 9

14. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Use the Vertical Line Test to determine whether y is a function of x. Describe how you can use the graphing utility to produce the given graph. Example 10

15. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Increasing: positive slope Decreasing: negative slope Constant: zero slope

16. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Determine the open intervals on which the function is increasing, decreasing or constant. Example 11

17. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. (A) Use a graphing utility to graph the function. (b) Determine the open intervals on which the function is increasing, decreasing or constant. Example 12 y = x 3

18. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. (A) Use a graphing utility to graph the function. (b) Determine the open intervals on which the function is increasing, decreasing or constant. Example 13 y = x 3 – 3x

19. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Section 1.3, Definitions of Relative Minimum and Relative Maximum

20. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Use a graphing utility to approximate any relative minimum or relative maximum values of the function. Example 14 f(x) = 3x 2 – 4x – 2

21. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Use a graphing utility to approximate any relative minimum or relative maximum values of the function. Example 15 f(x) = -x 3 + x

22. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. HW #61 pg 38-39 (1-41 odd…37-41 only part b)

23. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Test for Even and Odd Functions A function is even if, for each x in the domain of f, f(-x) = f(x). A function is odd if, for each x in the domain of f, f(-x) = -f(x). **Note: Unlike a number, a function does not have to be even or odd.**

24. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Algebraically determine whether the function is even, odd, or neither. Example 16 f(x) = |x|

25. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Algebraically determine whether the function is even, odd, or neither. Example 17 h(x) = x 3 - 5

26. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Use a graphing utility to determine whether the function is even, odd, or neither. Example 18

27. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. Use a graphing utility to determine whether the function is even, odd, or neither. Example 19

28. Essential Question: How do you find the domain and range of a function algebraically? How do you determine if a function is even or odd? Students will write a summary describing domain and range of a function and include how to determine if a function is even or odd. HW #62 pg 39-41 (31-49 odd, 59-65 odd, 73-85 odd, 95-100 all)