4.3 Function Rules, Tables, and Graphs

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4.3 Function Rules, Tables, and Graphs. Standard: SWBAT understand relation and a function; determine if a given relation defines a function. Mini Quiz 35. 1. Is this relation a function: {(5, 3), (-2, 3), (5, 3), (4, 3)}? Explain. 2. Find the domain and range of the relation in problem 1.

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## 4.3 Function Rules, Tables, and Graphs

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### 4.3 Function Rules, Tables, and Graphs

Standard: SWBAT understand relation and a function; determine if a given relation defines a function

Mini Quiz 35

1. Is this relation a function: {(5, 3), (-2, 3), (5, 3), (4, 3)}? Explain.

2. Find the domain and range of the relation in problem 1.

3. Is this relation a function? Explain.

Quick Review

1. How do you find the domain and the range?

Domain are the x’s, Range are the y’s

2. How do you tell if a relation is a function?

“Every x has only oney”. Check if x repeats/the vertical line test.

3. a) Is this a function? Why? {(3, 0), (-2, 1), (0, -1), (-3, 2)}

Yes, x doesn’t repeat.

b) Find the domain and range.

Domain: 3, -2, 0, -3 Range: 0, 1, -1,2

4. a) Is the table a function? Why?

No, x repeats and you get two different y

b) Find the domain and range.

Domain: -3, 6, 8 Range: -5, 7, 4, -2

Evaluating a Function Rule

The notation f(x) is the same as y (i.e. f(x) = y)

1. Evaluate f(x) = -3x – 10 for the domain {6}

f(6) = -3(6) – 10

f(6) = -18 – 10

f(6) = -28

Evaluating a Function Rule

The notation f(x) is the same as y (i.e. f(x) = y)

2. Evaluate f(x) = -x – 6 for the domain {-4}

f(-4) = -(-4) – 6

f(-4) = 4-6

f(-4) = -2

Evaluating a Function Rule

The notation f(x) is the same as y (i.e. f(x) = y)

3. Evaluate f(x) = x – 10 for the domain {-2}

f(-2) = (-2) – 10

f(-2) = -1 – 10

f(-2) = -11

Graphing Equations using a Table

Directions:

• Pick a number to plug in for x (usually “0”)
• Replace the x and calculate y
• Graph the ordered pair
• Repeat steps 1 - 3 at least 2 more times (to get the shape of the graph)
• Connect the points to draw the graph
Using Tables

Find the domain and range.

4. Model the function rule y = 2x - 3

x

2x - 3

y

0

2(0) – 3

= 0 – 3

-3

1

2(1) - 3

= 2 – 3

-1

-1

2(-1) - 3

= -2 – 3

-5

Using Tables

Find the domain and range.

5. Model the function rule f(x) = - 2x + 5

x

-2x + 5

f(x)

Using Tables

Find the domain and range.

6. Model the function rule y = - x + 1

- x + 1

x

y

Domain and Relations

Graph the function and determine the domain and range.

7. y = |x|

Domain and Relations

Graph the function and determine the domain and range.

8. f(x) =

Wrap Up
• Evaluating Function
• Using a Table to Graph
• Determining Domain and Function
• Determining Domain and Range

HW: P. 190 #1-17 odd, 21, 25, 61-67 all

DLUQ: What do you need to make to graph a function?