1. Relations and Functions
ALGEBRA 1 LESSON 5-2
(For help, go to Lessons 1–9 and 1–2.)
Graph each point on a coordinate plane.
1. (2, –4) 2. (0, 3) 3. (–1, –2) 4. (–3, 0)
Evaluate each expression.
5. 3a – 2 for a = – for x = x2 for x = 6
x + 3 –6
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2. Relations and Functions
ALGEBRA 1 LESSON 5-2
Solutions 1. 2. 3. 4.
5. 3a – 2 for a = –5: 3(–5) – 2 = –15 – 2 = –17
for x = 3: = = –1
7. 3x2 for x = 6: 3 • 62 = 3 • 36 = 108
x + 3 –6
3 + 3 6
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3. Relations and Functions
ALGEBRA 1 LESSON 5-2
Find the domain and the range of the ordered pairs.
age weight
domain: {12, 14, 16, 18} List the values in order. Do not repeat values.
range: {110, 120, 124, 125, 126}
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4. 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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5. Relations and Functions
ALGEBRA 1 LESSON 5-2
Determine whether each relation is a function.
a. {(4, 3), (2, –1), (–3, –3), (2, 4)}
The domain value 2 corresponds to two range values, –1 and 4.
The relation is not a function.
b. {(–4, 0), (2, 12), (–1, –3), (1, 5)}
There is no value in the domain that corresponds to more than one value of the range.
The relation is a function.
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6. Relations and Functions
ALGEBRA 1 LESSON 5-2
a. Evaluate ƒ(x) = –5x + 25 for x = –2.
ƒ(x) = –5x + 25
ƒ(–2) = –5(–2) + 25 Substitute –2 for x.
ƒ(–2) = Simplify.
ƒ(–2) = 35
b. Evaluate y = 4x2 + 2 for x = 3.
y = 4x2 + 2
y = 4(3)2 + 2 Substitute 3 for x.
y = 4(9) + 2 Simplify the powers first.
y = Simplify.
y = 38
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7. Relations and Functions
ALGEBRA 1 LESSON 5-2
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}.
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8. Relations and Functions
ALGEBRA 1 LESSON 5-2
1. a. Find the domain and range of the ordered pairs (1, 3), (–4, 0), (3, 1), (0, 4), (2, 3).
b. Use mapping to determine whether the relation is a function.
domain: {–4, 0, 1, 2, 3} range: {0, 1, 3, 4}
The relation is a function.
2. Use the vertical-line test to determine whether each relation is a function. a. b. no
yes
3. Find the range of the function ƒ(g) = 3g – 5 for the domain {–1.5, 2, 4}.
{–9.5, 1, 7}
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9. Function Rules, Tables, and Graphs
ALGEBRA 1 LESSON 8-6,7
(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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10. Function Rules, Tables, and Graphs
ALGEBRA 1 LESSON 8-6,7
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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11. Function Rules, Tables, and Graphs
ALGEBRA 1 LESSON 8-6,7
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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12. Function Rules, Tables, and Graphs
ALGEBRA 1 LESSON 8-6,7
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)
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13. Function Rules, Tables, and Graphs
ALGEBRA 1 LESSON 8-6,7
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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14. Function Rules, Tables, and Graphs
ALGEBRA 1 LESSON 8-6,7
(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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15. Function Rules, Tables, and Graphs
ALGEBRA 1 LESSON 8-6,7
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.
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16. Writing a Function Rule
ALGEBRA 1 LESSON 8-6,7
(For help, go to Lesson 8-6,7.)
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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17. Writing a Function Rule
ALGEBRA 1 LESSON 8-6,7
Solutions 1. 2. 3. 4. 5. 6.
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18. Writing a Function Rule
ALGEBRA 1 LESSON 8-6,7
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
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19. Writing a Function Rule
ALGEBRA 1 LESSON 8-6,7
Write a function rule for each table.
x ƒ(x)
2 8
4 10
6 12
8 14 a.
Ask yourself, “What can I do to 2 to get 8, 4 to get 10, ...?”
You add 6 to each x-value to get the ƒ(x) value.
Relate:    equals plus 6
Write: =
ƒ(x) x
A rule for the function is ƒ(x) = x + 6.
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20. Writing a Function Rule
ALGEBRA 1 LESSON 8-6,7
(continued) b.
x y
1 2
2 5
3 10
4 17
Ask yourself, “What can I do to 1 to get 2, 2 to get 5, ?”
You multiply each x-value times itself and add 1 to get the y value.
Relate:    equals plus 1
Write: = x2 y
x times itself
A rule for the function is y = x2 + 1.
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21. Writing a Function Rule
ALGEBRA 1 LESSON 8-6,7
The journalism class makes $25 per page of advertising in the yearbook. If the class sells n pages, how much money will it earn?
a. Write a function rule to describe this relationship.
Relate:    is  25  times  
money earned
number of pages sold
Define: Let = number of pages sold. n
Let = money earned.
P(n)
Write: = 25 •
The function rule P(n) = 25n describes the relationship between the number of pages sold and the money earned.
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22. Writing a Function Rule
ALGEBRA 1 LESSON 8-6,7
(continued)
b. The class sold 6 pages of advertising. How much money did the class make?
P(6) = 25 • 6 Substitute 6 for n.
P(6) = 150 Simplify.
P(n) = 25 • n
The class made $150.
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23. Writing a Function Rule
ALGEBRA 1 LESSON 8-6,7
The choir spent $100 producing audio tapes of its last performance and will sell the tapes for $5.50 each. Write a rule to describe the choir’s profit as a function of the number of tapes sold.
Relate: is $5.50 times minus cost of tape production
total profit
tapes sold
Define: Let = number of tapes sold. t
Let = total profit.
P(t)
Write: = • – 100
The function rule P(t) = 5.5t – 100 describes the profit as a function of the number of tapes sold.
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24. Writing a Function Rule
ALGEBRA 1 LESSON 8-6,7
1. Write a function rule for each table.
x y
–1 –5
0 0
1 5
2 10 a.
x ƒ(x)
–1 –4
0 –3
1 –2
2 –1 b.
y = 5x
ƒ(x) = x – 3
2. Write a function rule to describe each relationship.
a. the total cost T(c) of c pounds of apples at $.82 a pound
b. a scale model s of a moth m that is 6 times the actual size of the moth
T(c) = 0.82c
s(m) = 6m
3. You borrow $60 to buy a bread-making machine. You charge customers $1.50 a loaf for your special bread. Write a rule to describe your profit as a function of the number n of loaves sold.
P(n) = 1.5n - 60
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