1. 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: y x 5 -5 y x 5 -5 y x 5 -5

2. 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 – ) all real numbers
a) 0, b) -0.75, c) x2 + 2x 59) All real #s, t ≠0
30c) √x ) All real #s, y ≥ 10
31c) 1/ (y2 + 6y) ) -1 ≤ x ≤ 1
33c) All real #s, x ≠ 0, x ≠ -2
35. a) -1, b) 2, c) 6
36. a) 6, b) 3, c) 10

3. 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 #1-5, 9-12, 15, 17, 23, 33-35
Bring calculator next class!

4. 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

5. 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 = ?”

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

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

8. 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.

9. 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.