Lesson 1: Introduction to Functions Answer Key
Lesson 1 Answer Keys – Winter 2015
Lesson 1 You-Try Problems
3. a) Input: Time (in years); Output Value: (in
dollars)
b) Dependent: V ; Independent: t
c) Two years after purchase, the value of the
car was $24630.
d) Yes. Value of the car is a function of
time. Each input is paired with a single
output.
6. Functions: A, B, D, F, Not Functions: C,
E
12. a) f(2) = -10, (2, -10)
b) f(−11
3) = 7, (−
11
3, 7)
c) f(-3) = 5, (-3, 5)
d) f(8/3) = -12. (8/3, -12)
e) f(-x) = 3x – 4
f) f(x – 5) = -3x + 11
19.
a) Domain:{7, 8, 11}, Range: {8, 12, 21}
b) Domain: {3, 6, 8}, Range: {33, 42, 51}
c) Domain: −7 ≤ 𝑥 < 4, [−7,4), Range:
−6 ≤ 𝑓(𝑥) < 7, [−6,7)
22.
a) C(x) = 3.25x + 30.00
b) 0 miles, 25miles
c) $30, $111.25
d) If 60 miles are towed, the cost is $225.
e) (15, 78.75) If 15 miles are towed, the
cost is $78.75.
f) x = 0 (0, 30) If 0 miles are towed, the cost
is $30.
23. a) t = time in years
b) V(t) = value in $
c) 1200, 600, 0
d) Graph should include labels for plotted
points and axes. Points should be connected.
Graph should not extend beyond the
starting/ending points from the table.
e) 8 years old
f) $1000
g) 120 t years or [0, 12]
h) $ 0 ( ) $1200V t or [0, 1200]
Lesson 1 Practice Problems
1.1: What is a function? Pages 32 – 35
1: a) time in minutes, t, distance in km, D
b) {(0, 0), (20, 4003), (40, 9452), (60, 14232), (80, 18700), (100, 20200), (120, 20200)}
c) Forty minutes after being launched, the satellite is 9452 km from the Earth
d) Yes. Every time value has exactly one distance value.
e) No. The distance value 20,200 km corresponds to two time values, 100 minutes and 120
minutes.
Lesson 1: Introduction to Functions Answer Key
2: a) time in minutes, t, number of Gene copies, G
b) {(0, 52), (3, 104), (5, 165), (6, 208), (8, 330), (10, 524), (12, 832)}
c) After six minutes of observation, there are 208 gene copies.
d) Yes. Every time value has exactly one number of Gene Copies value.
e) Yes. Every number of gene copies has exactly one corresponding time value.
3: a) time in minutes, t, number of homework problems completed, H
b) {(0, 0), (10, 3), (20, 8), (30, 8), (40, 15), (50, 17), (60, 20)}
c) After forty minutes, Tara completed 15 homework problems.
d) Yes. Every time value has exactly one corresponding number of homework problems
completed.
e) No. The number of homework problems completed value of 8 corresponds to two time
values, 20 minutes and 30 minutes.
4: a) time in minutes, t, number of hotdogs eaten, H
b) {(0, 0), (1, 8), (3, 23), (5, 37), (7, 50), (9, 63), (10, 68)}
c) After seven minutes, the competitive hotdog eater had eaten 50 hotdogs.
d) Yes. Every time value has exactly one corresponding number of hotdogs eaten
e) Yes. Every number of hot dogs eaten has exactly one corresponding time value
1.2: Multiple representations of functions Pages 36 – 39
5: a) Yes b) Yes c) No d) Yes e) No
6: a) No b) Yes c) No d) Yes e) No f) Yes g) No
7: a) Yes b) Yes c) Yes d) No e) No f) No
8: Results Vary
9: a) Constant b) Decreasing c) Increasing d) Increasing e) Decreasing f) Constant
10: a) Increasing b) Decreasing c) Constant d) Constant e) Decreasing f) Increasing
Section 1.3: Function Evaluation Pages 39 – 47
11: a) 4 b) 7 c) 6
12: a) 20 b) 6 c) 14
13: a) 18 b) 13 c) 4
14: a) −18 b) −4 c) 0
Lesson 1: Introduction to Functions Answer Key
15: a) −2𝑥 + 6 b) −1
2𝑥 + 6 c) −𝑥 + 9
16: a) 14 − 6𝑡 b) 14 −1
2𝑡 c) 6 − 2𝑡
17: a) 8𝑐2 + 6𝑐 + 4 b) 2𝑐2 − 7𝑐 + 9 c) 2𝑥2 + 5𝑥 + 6
18: a) Given: Input Finding: Output Ordered Pair: (2, 0)
b) Given: Output Finding: Input Ordered Pair: (3, 3)
c) Given: Input Finding: Output Ordered Pair: (−4, −18)
d) Given: Output Finding: Input Ordered Pair: (−2, −12)
19: a) Given: Input Finding: Output Ordered Pair: (4,11
2)
b) Given: Output Finding: Input Ordered Pair: (7
3, 3)
c) Given: Input Finding: Output Ordered Pair: (−8, −25
2)
d) Given: Output Finding: Input Ordered Pair: (−2, −7
2)
20: a) −7 b) 7 c) 14
21: a) Given: Output Finding: Input Ordered Pair: (0, −12)
b) Given: Input Finding: Output Ordered Pair: (−4,3)
c) Given: Output Finding: Input Ordered Pair: (−4,3)
d) Given: Input Finding: Output Ordered Pair: (2, −17)
22: a) Given: Output Finding: Input Ordered Pair: (0, 5)
b) Given: Input Finding: Output Ordered Pair: (−2,3)
c) Given: Output Finding: Input Ordered Pair: (−2,3)
d) Given: Input Finding: Output Ordered Pair: (3,9)
23: a) Given: Output Finding: Input Ordered Pairs: (0, 5), (6,5)
b) Given: Input Finding: Output Ordered Pair: (2, −3)
c) Given: Output Finding: Input Ordered Pair: (1,0), (5,0)
d) Given: Input Finding: Output Ordered Pair: (3, −4)
Lesson 1: Introduction to Functions Answer Key
24. 32xy
a.
x – 3 – 1 0 1 3
y – 9 – 5 – 3 – 1 3
b.
25. 43x)(xf
a.
x – 3 – 1 0 1 3
y 13 8 4 1 – 5
b.
Section 1.4: Domain and Range Pages 47 – 50
26: a) Domain: {3, 5, 7, 9, 11, 13} Range: {−2, −1, 8, 4}
b) Domain: {−2, −1, 0, 1} Range: {−5}
c) Domain: {−3, 1, 0, 4} Range: {2, −5, −3, −2}
27: a) Domain: {−10, −5, 0, 5, 10} Range: {3, 8, 12, 15, 18}
b) Domain: {−20, −10, 0, 10, 20, 30} Range: {−4, 14, 32, 50, 68, 86}
c) Domain: {1, 2, 3, 4, 8, 9, 10, 11, 12} Range: {54, 62, 66, 69, 72, 73, 74}
Lesson 1: Introduction to Functions Answer Key
28: a) Domain: Inequality Notation −∞ < 𝑥 < ∞, Interval Notation (−∞, ∞)
Range: Inequality Notation −∞ < 𝑦 < ∞, Interval Notation (−∞, ∞)
b) Domain: Inequality Notation−8 ≤ 𝑥 ≤ 6, Interval Notation [−8, 6]
Range: Inequality Notation−4 ≤ 𝑦 ≤ 4, Interval Notation [−4,4]
c) Domain: Inequality Notation−6 ≤ 𝑥 ≤ 7, Interval Notation [−6, 7]
Range: Inequality Notation−3 ≤ 𝑦 ≤ 2, Interval Notation [−3,2]
d) Domain: Inequality Notation−8 < 𝑥 ≤ 7, Interval Notation (−8, 7]
Range: Inequality Notation−5 ≤ 𝑦 < 4, Interval Notation [−5,4)
Section 1.5: Applications of Functions Pages 51 – 55
29: a) 𝐶(𝑤) = 0.50𝑤 + 20
b) 0 ≤ 𝑤 ≤ 200
c) 20 ≤ 𝐶(𝑤) ≤ 120
d) w 0 50 150 200
C(w) 20 45 95 120
e) 𝐶(50) = 45. When 50 windows are washed, the total cost is $45.
f) 𝐶(50) = 45. When 50 windows are washed, the total cost is $45.
g) Solve 45 = 0.50𝑤 + 20 for w.
30: a)
b) (0,0) 𝑜𝑟 𝑃(0) = 0, (8,96)𝑜𝑟 𝑃(8) = 96
c) Input Quantity: time in hours
Practical Domain: Inequality Notation 0 ≤ 𝑡 ≤ 8, Interval Notation [0, 8]
d) Output Quantity: number of pizzas made
Lesson 1: Introduction to Functions Answer Key
Practical Domain: Inequality Notation 0 ≤ 𝑃(𝑡) ≤ 96, Interval Notation [0, 96]
e) 𝑃(3) = 36. The number of pizzas made in 3 hours is 36.
f) 𝑃 (55
6) = 70. Seventy pizzas are made in 5
5
6 ℎ𝑜𝑢𝑟𝑠 or 5 hrs and 50 minutes.
31: a) x is used for the input
b) The number of years since 1900
c) L is used for the output
d) The life expectancy for males in years
e) x 0 20 40 60 80 100 120
L(x) 48.3 53.7 59.1 64.5 69.9 75.3 80.7
f) Practical Domain: 0 ≤ 𝑥 ≤ 120
g) Practical Range: 48.3 ≤ 𝐿(𝑥) ≤ 80.7
h) 𝐿(43.3) ≈ 60. 1900 + 43.3 = 1943.3, so the man was born in 1943.
Lesson 1: Introduction to Functions Answer Key
Section 1.1: What is a Function?
Media Example 1, workbook page 11
Lesson 1: Introduction to Functions Answer Key
Section 1.2: Multiple Representations of Functions
Media Example 4, workbook page 14
Lesson 1: Introduction to Functions Answer Key
Media Example 7, workbook page 16
Lesson 1: Introduction to Functions Answer Key
Section 1.3: Function Notation
Media Example 9, workbook page 18
Lesson 1: Introduction to Functions Answer Key
Media Example 11, workbook page 19
Lesson 1: Introduction to Functions Answer Key
Media Example 13, workbook page 21
Lesson 1: Introduction to Functions Answer Key
Media Example 14, workbook page 21
Lesson 1: Introduction to Functions Answer Key
Media Example 15, workbook page 22
Lesson 1: Introduction to Functions Answer Key
Media Example 16, workbook page 23
Lesson 1: Introduction to Functions Answer Key
Section 1.4: Domain and Range
Media Example 17, workbook page 24
Lesson 1: Introduction to Functions Answer Key
Section 1.5: Applications of Functions
Media Example 20, workbook page 26
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