1. Relations and Functions
ALGEBRA 1 LESSON 5-2
Use the vertical-line test to determine whether the relation {(3, 2), (5, –1), (–5, 3), (–2, 2)} is a function.
Step 1: Graph the ordered pairs on a coordinate plane.
Step 2: Pass a pencil across the graph. Keep your pencil straight to represent a vertical line.
A vertical line would not pass through more than one point, so the relation is a function.
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2. Function Rules, Tables, and Graphs
ALGEBRA 1 LESSON 5-3
(For help, go to Lesson 5-2.)
Graph the data in each table.
x y
–3 –7
–1 –1
0 2
2 8 1.
x y
–3 4
–2 0
0 –2
2 4 2.
x y
–4 –3
0 –2
2 –1.5
4 –1 3.
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3. Function Rules, Tables, and Graphs
ALGEBRA 1 LESSON 5-3
1. Graph the points: 2. Graph the points:
(–3, –7) (–3, 4)
(–1, –1) (–2, 0)
(0, 2) (0, –2)
(2, 8) (2, 4)
Solutions
3. Graph the points:
(–4, –3)
(0, –2)
(2, –1.5)
(4, –1)
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4. Function Rules, Tables, and Graphs
ALGEBRA 1 LESSON 5-3
Model the function rule y = using a table of values and a graph. 1 3 x
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 2: Plot the points for the ordered pairs.
Step 3: Join the points to form a line.
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5. Function Rules, Tables, and Graphs
ALGEBRA 1 LESSON 5-3
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.
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)
5-3

6. Function Rules, Tables, and Graphs
ALGEBRA 1 LESSON 5-3
a. 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.
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7. Function Rules, Tables, and Graphs
ALGEBRA 1 LESSON 5-3
(continued)
b. Graph the function ƒ(x) = x2 + 2.
x ƒ(x) = x2 + 2 (x, y)
–2 ƒ(–2) = = 6 (–2, 6)
–1 ƒ(–1) = = 3 (–1, 3)
0 ƒ(0) = = 2 ( 0, 2)
1 ƒ(1) = = 3 ( 1, 3)
2 ƒ(2) = = 6 ( 2, 6)
Make a table of values.
Then graph the data.
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8. Function Rules, Tables, and Graphs
ALGEBRA 1 LESSON 5-3
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.
3. Graph ƒ(x) = 2x2 – 2.
5-3

9. Writing a Function Rule
ALGEBRA 1 LESSON 5-4
(For help, go to Lesson 5-3.)
Model each rule with a table of values.
1. f(x) = 5x – 1 2. y = –3x g(t) = 0.2t – 7
4. y = 4x f(x) = 6 – x 6. c(d) = d + 0.9
Evaluate each function rule for n = 2.
7. A(n) = 2n – 1 8. f(n) = –3 + n – 1 9. g(n) = 6 – n
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10. Writing a Function Rule
ALGEBRA 1 LESSON 5-4
Solutions 1. 2. 3. 4. 5. 6.
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11. Writing a Function Rule
ALGEBRA 1 LESSON 5-4
Solutions (continued)
7. A(n) = 2n – 1 for n = 2:
A(2) = 2(2) – 1 = 4 – 1 = 3
8. f(n) = –3 + n – 1 for n = 2:
f(2) = –3 + 2 – 1 = –1 – 1 = –2
9. g(n) = 6 – n for n = 2:
g(2) = 6 – 2 = 4
5-4