lesson 1 answer keys winter 2015 - north seattle...

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.


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


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)


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}


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


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.


Section 1.1: What is a Function?

Media Example 1, workbook page 11


Section 1.2: Multiple Representations of Functions



Section 1.3: Function Notation



Section 1.4: Domain and Range



Section 1.5: Applications of Functions


lesson 1 answer keys winter 2015 - north seattle...

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