Warm-up: Determine whether the graph of y is a function of x: 1. 2. 3. September 20, 2011 At the end of today, you will be able to: Find the zeros of functions. Determine intervals on which functions are increasing or decreasing and determine relative maximum and relative minimum values of functions. Warm-up: Determine whether the graph of y is a function of x: 1. 2. 3. y x 5 -5 y x 5 -5 y x 5 -5

Check HW 1.4 5. Yes, each input has exactly one output value 9. a) Function, b) Not a function, c) Function, d) Not a function 25. a) -1, b) -9, c) 2x – 5 57) all real numbers a) 0, b) -0.75, c) x2 + 2x 59) All real #s, t ≠0 30c) √x + 2 61) All real #s, y ≥ 10 31c) 1/ (y2 + 6y) 63) -1 ≤ x ≤ 1 33c) 65 All real #s, x ≠ 0, x ≠ -2 35. a) -1, b) 2, c) 6 36. a) 6, b) 3, c) 10

Lesson 1.5 Analyzing Graphs of Functions The graph of a function is the collection of ordered pairs (x,f(x)), such that x is in the domain of f. Remember f(x) is the same as the y values! HW 1.5: Pg. 61-62 #1-5, 9-12, 15, 17, 23, 33-35 Bring calculator next class!

Before we start, do you remember Interval Notation For example: 20 -15 -5 5 15 -20 -10 10 “ ( “ -- does not include the value “ [ “ -- includes the value

Same as saying: -1 ≤ x < 5 Finding the Domain and Range of a Function Example 1: Use the graph to answer the following: a) Find the domain and range: The domain is all the possible x values. Same as saying: -1 ≤ x < 5 Domain: [-1, 5) The range is all the possible y values. Same as saying: -3 ≤ y ≤ 3 Range: [-3, 3] b) Find the indicated values for the following: f(-1) = f(2) = 1 -3 “When x = -1, y = ?” “When x = 2, y = ?”

Practice: Find the Domain and Range 1. 2. 3. Find f(0) for both graphs. y = sin (x) Domain: [-4, ∞) Range: [0, ∞) f(0) = 2 Domain: [-∞, ∞) Range: [-1, 1] f(0) = 0

Finding the Zeros of a Function “Find x when y = 0” Example 3: Set the equation equal to 0: 10 – x2 = 0 +x2 +x2 10 = x2 ( )2 ( )2 Practice: f(x) = 3x2 + x – 10 5)

Example 4: Increasing and Decreasing Functions Determine the intervals over which the function is increasing, decreasing, or constant. Analyze where y values of the graph go up and down. Increasing at (-∞, 0) Constant at [0, 2] Decreasing at [2, ∞) Increasing at (-∞, -1] Decreasing at [-1, 1] Increasing at [1, ∞) The function is increasing over the entire real line.

Graphing Calculator Activity Pg. 63 #49-52 How to find the relative minimum and maximum values in your calculator. Graph the function in “Y =“ 2nd  Calc Select whether you are finding the min or max Left Bound? (Place the cursor to the left of the min/max, then press enter) Right Bound? (Place cursor to the right of the min/max, then press enter) Guess? (Pres enter) It should give you the min or max of the function *This should also work to find the “zeros” in your function.