September 17, 2012Analyzing Graphs of Functions

Warm-up: Talk to your group about the Distance Formula

worksheet given last week. Make sure you understand how it was derived. You should be able to derive it on your own without the worksheet.

1. Find the distance and midpoint between (3, -1) and (10, 6).

2. Write the equation of a circle whose endpoints of the diameter are (-4, -1) and (4, 1)

What do you remember about functions?Determine whether the graph of y is a function of x:*Hint: Vertical Line Test

1. 2. 3.

y

x5

5

-5

-5

y

x5

5

-5

-5

y

x5

5

-5

-5

What does it mean to “find the zeros” of a function?4. Find the zero of the function: a) f(x) = 3x2 + 22x – 16 b)

g(x) 10 x 2

Do you remember Interval Notation?Write the following sets in interval notation, then graph

it on a number line.For example: {x| x > 5} ---> (5, ∞)

x x 3

x x 3

x x 3

x x 3“ ( “ -- does not include the value“ [ “ -- includes the value

CW 1.5: Pg. 62 #9-12, 15-24Bring calculator next class!

September 19, 2012We want the Funk…Gotta have those Func…tions!

Warm-up: Find the zeroes and state the domain of the function.

1. f(x) = x3 – x2 – 25x + 25

2.

f (x) 2x 2 93 x HW 1.5: Pg. 61-62 #1-5,

32-38even, 67, 69Quiz next class!

Lesson 1.5Analyzing 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!

Finding the Domain and Range of a FunctionExample 1: Use the graph to answer the following:

a) Find the domain and range:The domain is all the possible x values.

Domain: [-1, 5) Same as saying: -1 ≤ x < 5

Range: [-3, 3] Same as saying: -3 ≤ y ≤ 3

The range is all the possible y values.

b) Find the indicated values for the following: f(-1) = f(2)

= “When x = -1, y = ?” “When x = 2, y = ?”

Practice:Find the Domain and Range

1. 2.

3. Find f(0) for both graphs.

4 xy y = sin (x)

Example 3: 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.

The function is increasing over the entire real line.

Increasing at (-∞, -1)Decreasing at (-1, 1)Increasing at (1, ∞)

Increasing at (-∞, 0)Constant at [0, 2]Decreasing at (2, ∞)

Graphing Calculator ActivityPg. 63 #49, 51, 53, 54

Sketch each graph belowHow 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? (Press enter)- It should give you the min or max of the function*This should also work to find the “zeros” in your function.

Example 4: Determine the intervals for which f(x) ≥ 0

Example 5: Finding the average rate of change of the function.Find the rate of change from x1 = 0 to x2 = 3 for the

function f(x) = 3x + 8

On your own, find the rate of change from x1 = 1, x2 = 5 for f(x) = x2 – 2x + 8