1. Lesson 4-3 Warm-Up

2. “Function Rules, Tables, and Graphs” (4-3)
What is a “function rule”? What is a “function table”?
Function Rule: an equation that describes a function – You can think of a function as function rule as an input-output machine If you know the input values, you can use a function rule to find the output values (in other words, the output values depend on the input values). Function Table: a table in which shows the relation between the input and output values. Example: The following function table shows the relation of the above function rule.

3. “Function Rules, Tables, and Graphs” (4-3)
What is “function notation”? What are the “independent and dependent variable”?
Function Notation: writing a function in the form of f(x) , which is read “f of x” [in other words, replace y with f(x), g(x), h(x) or something similar] Example: Instead of y = 3x + 4, write f(x) = 3x + 4 to show that this is a function rule. Independent Variable (its value doesn’t depend on another number): the input, or x, values Dependent Variable (its value depends on another number, the independent varable): the output, or y, values

4. Function Rules, Tables, and Graphs
LESSON 4-3
Additional Examples
Evaluate the function rule ƒ(g) = –2g + 4 to find the range for the domain {–1, 3, 5}.
ƒ(g) = –2g + 4
ƒ(–1) = –2(–1) + 4
ƒ(–1) = 2 + 4
ƒ(–1) = 6
ƒ(g) = –2g + 4
ƒ(3) = –2(3) + 4
ƒ(3) = –6 + 4
ƒ(3) = –2
ƒ(g) = –2g + 4
ƒ(5) = –2(5) + 4
ƒ(5) = –10 + 4
ƒ(5) = –6
The range is {–6, –2, 6}.

5. Model the function rule y = + 2 using a table of values and a graph. x
Function Rules, Tables, and Graphs
LESSON 4-3
Additional Examples
Model the function rule y = using a table of values and a graph. 1 3 x
Step 2: Plot the points for the ordered pairs.
Step 1: Choose input value for x. Evaluate to find y.
x (x, y)
–3 y = (–3) + 2 = 1 (–3, 1)
 0 y = (0) + 2 = 2 (0, 2)
 3 y = (3) + 2 = 3 (3, 3)
y = x + 2 1 3
Step 3: Join the points to form a line.
(3, 3)
(–3, 1)
(0, 2)

6. Function Rules, Tables, and Graphs
LESSON 4-3
Additional Examples
At the local video store you can rent a video game for $3. It costs you $5 a month to operate your video game player. The total monthly cost C(v) depends on the number of video games v you rent. Use the function rule C(v) = 5 + 3v to make a table of values and a graph.
(2, 11)
v C(v) = 5 + 3v (v, C(v))
0 C(0) = 5 + 3(0) = 5 (0, 5)
1 C(1) = 5 + 3(1) = 8 (1, 8)
2 C(2) = 5 + 3(2) = 11 (2, 11)
(1, 8)
(0, 5)

7. Graph the function y = |x| + 2.
Function Rules, Tables, and Graphs
LESSON 4-3
Additional Examples
Graph the function y = |x| + 2.
Make a table of values.
x y = |x| + 2 (x, y)
–3 y = |–3| + 2 = 5 (–3, 5)
–1 y = |–1| + 2 = 3 (–1, 3)
0 y = |0| + 2 = 2 ( 0, 2)
1 y = |1| + 2 = 3 ( 1, 3)
3 y = |3| + 2 = 5 ( 3, 5)
Then graph the data.
(-3, 5)
(3, 5)
(-1, 3)
(1, 3)
(0, 2)

8. Find the domain of the relation y = . Is the relation a function?
Function Rules, Tables, and Graphs
LESSON 4-3
Additional Examples 1
2 – x
Find the domain of the relation y = Is the relation a function?
The function is not defined for x = 2. So the domain is {x:x ≠ 2}. Since each value in the domain corresponds to exactly one value in the range. The relation is a function.

9. 1. Model y = –2x + 4 with a table of values and a graph.
Function Rules, Tables, and Graphs
LESSON 4-3
Lesson Quiz
1. Model y = –2x + 4 with a table of values and a graph.
x y = –2x + 4 (x, y)
–1 y = –2(–1) + 4 = 6 (–1, 6)
0 y = –2(0) + 4 = 4 (0, 4)
1 y = –2(1) + 4 = 2 (1, 2)
2 y = –2(2) + 4 = 0 (2, 0)
2. Graph y = |x| – 2.