Linear Relationships and Functions

Northwest Vista College Mathematics Department

Linear Relationships and Functions

Prep for Percent and Proportion

1. 1. 1. [latex]\frac18[/latex]
    2. [latex]\frac38[/latex]
    3. [latex]\frac68;\;\text{equivalent}\;\text{to}\;\frac34[/latex]
    4. [latex]\frac26[/latex]
    5. [latex]\frac23[/latex]
    6. [latex]\frac34;\;\text{equivalent}\;\text{to}\;\frac68[/latex]
    7. [latex]1\frac23[/latex]
    1. Answers may vary.
    2. It is necessary to write 1 if it is the part (not the whole) in a ratio.
1. 1. Part = 8; Whole = 22.58; Fraction [latex]=\frac8{22.58}[/latex]
  2. Part = 58; Whole = 82; Fraction [latex]=\frac{58}{82}[/latex]
  3. Part = 4,630; Whole = 15,435; Fraction [latex]=\frac{4,630}{15,435}[/latex]
  4. Part = 212; Whole = 802; Fraction [latex]=\frac{212}{802}[/latex]
  5. Part = 170; Whole = 950; Fraction [latex]=\frac{170}{950}[/latex]
  6. Part = [latex]2\frac12[/latex]; Whole = [latex]5\frac34[/latex]; Fraction [latex]=\frac{2{\displaystyle\frac12}}{5{\displaystyle\frac34}}[/latex]

1. 1. 1. subtraction
    2. multiplication
    3. division
    4. addition
    5. multiplication
    6. addition (-7) or subtraction (7)
    7. division
    8. multiplication
    9. multiplication and division
    10. multiplication
    11. multiplication and division
    12. multiplication and division
    1. subtraction
    2. subtract 5 from both sides; [latex]x=14[/latex]
    3. [latex]x=55[/latex]
    1. addition
    2. add 5 to both sides; [latex]x=7[/latex]
    3. [latex]x=42[/latex]
    1. division
    2. divide both sides by 3; [latex]x=21[/latex]
    3. [latex]x=22[/latex]
    1. No. [latex]x-3[/latex] is held by subtraction;
      [latex]-3x[/latex] is held by multiplication
    2. add 3 to both sides; [latex]x=15[/latex]
    3. divide both sides by [latex]-3;x=-4[/latex]
    1. division
    2. multiplication
    3. multiply both sides by 4; [latex]x=60[/latex]
    4. [latex]x=100[/latex]
  2. multiplication, division; division, multiplication; [latex]x=25[/latex]
  3. multiplication; [latex]x=\frac15[/latex]
  4. [latex]x=20[/latex]

1. [latex]p=0.1[/latex]
2. [latex]n=150[/latex]
3. [latex]x=5200[/latex]
4. [latex]x=17.5[/latex]
5. [latex]x=21[/latex]
6. [latex]x=56[/latex]
7. [latex]t=20.4[/latex]
8. [latex]x=4[/latex]
9. [latex]x=3[/latex]
10. [latex]b=8[/latex]

Classwork: Percent and Proportion

1. Explain.
2. Explain.
1. 70
2. 17.5%
3. 62.5
4. 130
5. [latex]233.\overline3[/latex]
6. 555 students
7. 3.6%
8. 6.97%

1. 66 beats
2. 800 calories
3. 105.86 gallons

1. $209,300
2. $21.22
3. $1966.67
4. 62% decrease
5. 25% increase

1. 2 gal of 50%; 4 gal of 75%
2. 4 cups; 5%
3. [latex]3\frac14[/latex] cups of 2.77% fat
4. 35 pints; 5% salinity
5. 5 liters of 1%; The mixture is 1.57%

1. [latex]\approx0.96\%[/latex]
2. 2,250 people
3. 1,600 trout
4. $44.56
5. [latex]\approx67.07\%[/latex]
6. 52 games

Homework: Percent and Proportion

1. 1. 10.08
  2. 92
  3. [latex]\approx31.48\%[/latex]
  4. 3.12
  5. Explain.
  6. 1,234 students
  7. [latex]\approx71.4\%[/latex]
  8. An equation in which two ratios (fractions) are set equal
  9. Cross multiply and solve for the unknown
  1. t=20.4
  2. x=4
  3. x=3
  4. k=3
  5. b=8

1. 1. 3.75 miles
  2. $219,000
  3. [latex]3\frac13[/latex] hours
  4. 3,750 penguins
  5. 2.1 lbs
  6. 462 lbs
  7. 7,700 lbs
  8. 165 calories
  9. 19 ft
  10. 35 puppies, 20 adult dogs
  11. 630 frat men
  12. 51.3% are females
  13. $369.52
  14. $9.90 discount, $23.09 sale price
  15. $92.81 tax, $1,217.81
  16. $7.00 tip
  17. 49% decrease
  18. Explain

1. 4,000 gallons; 2.625% salinity
2. [latex]2\frac12[/latex] cup of 4% fat
3. [latex]1\frac34[/latex] cups; 1.7% alcohol
4. 3 quarts of whole milk; the mixture is 5.8% fat
5. liters of 1% low-fat; 1.8% fat in the mixture

Prep for Scientific Notation and Conversions

1. 1. 10
  2. 100
  3. 10,000
  4. 10,000,000
  5. Discussion may vary
  6. [latex]10^4[/latex]
  7. [latex]10^8[/latex]
  1. 0.1
  2. 0.01
  3. 0.0001
  4. 0.0000001
  5. Discussion may vary.
  6. [latex]10^{-5}[/latex]
  7. [latex]10^{-9}[/latex]

1. 700
2. 0.0003
3. 7,450,000
4. 0.000314

Classwork: Scientific Notation and Metric Conversions

Scientific Notation

1. [latex]3.54\times10^7[/latex]
2. [latex]9.876\times10^{-9}[/latex]
3. [latex]2,320,000[/latex]
4. [latex]0.0052[/latex]

Metric System Conversions

1. [latex]0.5[/latex] m
2. [latex]8,000[/latex] g
3. [latex]9100[/latex] L
4. [latex]98[/latex] mg
5. [latex]0.0091[/latex] L
6. [latex]720,000[/latex] mm
7. [latex]568,000[/latex] mg
8. [latex]98,000[/latex] µg
9. [latex]2,000,000[/latex] µg
10. [latex]40,000[/latex] cm²
11. [latex]250,000,000[/latex] cm³
12. [latex]130,400[/latex] km²

Homework: Scientific Notation and Metric Conversions

1. 1. [latex]3.04\times10^3[/latex]
  2. [latex]-4.789\times10^{-3}[/latex]
  3. [latex]7.18\times10^{-6}[/latex]
  4. [latex]3.108\times10^{6}[/latex]
  5. Many answers are possible.

1. 1. [latex]2.5\times10^{-3}[/latex]
  2. [latex]2.5[/latex] mg
  3. [latex]2500[/latex] µg
  4. Discuss.
2. [latex]5\times10^2[/latex] mL
3. [latex]1.6\times10^2[/latex] mm
4. [latex]1.04\times10^7[/latex] cm
5. [latex]4.8\times10^2[/latex] cm²
6. [latex]1.98\times10^{-3}[/latex] kg
7. [latex]2.5\times10^{-2}[/latex] km
8. [latex]1.6\times10^5[/latex] mm³
9. [latex]1.2\times10^{-5}[/latex] ML
10. France by [latex]136,033[/latex] km²

Prep for Imperial Conversions

1. 1. 90
  2. 19.3548
  3. 12,096
  4. [latex]\frac{5}{8}[/latex] or 0.625
  5. Compare with a classmate
  1. [latex]\frac{\cancel8}1\cdot\frac5{\cancel8}=5[/latex]
  2. [latex]\frac{\cancel{4.5}}1\cdot\frac7{\cancel{4.5}}=7[/latex]
  3. [latex]\frac{\cancelto{2}{10}}{1} \cdot \frac{3}{\cancel5} = 6[/latex]
  4. [latex]\frac{\cancelto{2}{12}}{1} \cdot\frac{\bcancel5}{\cancel6}\cdot\frac7{\bcancel5}=14[/latex]
  5. [latex]\frac{15}{\cancel8}\cdot\frac{\cancel8}{\bcancel7}\cdot\frac{\bcancel7}4=\frac{15}4[/latex]
  6. [latex]\frac91\cdot\frac21\cdot\frac{11}1=198[/latex]
  7. [latex]\frac{\cancel9}1\cdot\frac{10}{\cancel3}\cdot\frac5{\cancel3}=50[/latex]
  8. [latex]\frac{\cancel{25}}4\cdot\frac2{\cancel5}\cdot\frac2{\cancel5}=1[/latex]

[latex]72[/latex] yd
[latex]74[/latex] feet
[latex]64[/latex] m²
[latex]312[/latex] ft²
[latex]125[/latex] in³
[latex]936[/latex] ft³

1; 2 (square units); 3 (cubic units)

	Length (distance) 1 dimension	Area 2 dimensions	Volume 3 dimensions	Mass	Time	Imperial (British)	Metric
1. cm	✓						✓
2. cm³			✓				✓
3. in²		✓				✓
4. g				✓			✓
5. hm	✓						✓
6. dag				✓			✓
7. years					✓	✓
8. dL			✓				✓
9. dam²		✓					✓
10. mm³			✓				✓
11. m	✓						✓
12. mi	✓					✓

[latex]\frac{2.54\;cm}{1\;\text{in}},\;\text{length}[/latex]
[latex]\frac{12\;\text{in}}{1\;ft},\;\text{length}[/latex]
[latex]\frac{0.3048\;m}{1\;ft},\;\text{length}[/latex]
[latex]\frac{640\;\;\text{acres}}{1\;mi^2},\;\text{length}[/latex]
[latex]\frac{640\;\;\text{acres}}{1\;mi^2},\;\text{area}[/latex]
[latex]\frac{0.001\;m^3}{1L},\;\text{volume}[/latex]
[latex]\frac{3\;ft}{1yd},\;\text{length}[/latex]
[latex]\frac{9\;ft^2}{1yd^2},\;\text{area}[/latex]
[latex]\frac{29.5735\;cm^3}{1\;oz},\;\text{volume}[/latex]

Classwork: Imperial Conversions

1. Answers may vary.
2. Answers may vary.
3. 2 yds
4. 54.61 cm
5. 131.23 yd
6. 88,513.92 m
7. [latex]8.0645[/latex] cm²
8. [latex]46,609.2[/latex] ft²
9. 13056 oz
10. 6 lbs
11. [latex]864[/latex] in³
12. 259,200 sec
13. 6 years 3.34 months
14. 120 mi/day
15. 272.19 L/hr
16. [latex]2.998\times10^8[/latex] m/sec
17. Discuss with a classmate.

Applications of Conversions

1. [latex]1.58\times10^9[/latex] sec
2. [latex]226.04[/latex] ft²
3. [latex]2.58[/latex] sec
4. [latex]1,728[/latex] in
5. [latex]15,840[/latex] in²
6. [latex]7.33[/latex] ft/s
7. Mat’s bathtub fills faster
8. 7 lb, 10.05 oz

Homework: Imperial Conversions

1. 1. [latex]6.21[/latex] mi
  2. [latex]120,000,000[/latex] µg
  3. [latex]12,672[/latex] ft
  4. [latex]109.68[/latex] cm²
  5. [latex]804.4[/latex] mL
  6. [latex]2[/latex] ft
  7. [latex]10.57[/latex] pt
  8. [latex]25.4[/latex] cm
  9. [latex]20[/latex] lb
  10. [latex]525,600[/latex] min
  11. [latex]131.234[/latex] yd
  12. [latex]66,908,160[/latex] ft²
  13. [latex]23,562[/latex] in³
  14. [latex]5,297.2[/latex] ft³
  15. [latex]4.299[/latex] lb
  16. [latex]42.33[/latex] oz
  17. [latex]4.23[/latex] pt
  18. [latex]220.98[/latex] m
  19. [latex]25.1[/latex] gal
  20. [latex]26.82[/latex] m/s
  21. [latex]5.93\times10^{-6}[/latex] m³
  22. [latex]0.0283[/latex] m³
  23. [latex]14.2[/latex] mg/mm²
  24. [latex]82.4[/latex] mg/mm²

1. [latex]6.214[/latex] miles
2. Explain.
  1. No
  2. Explain.
  3. 27.8 mph
3. [latex]290.8[/latex] mph
4. [latex]750[/latex] mph
5. [latex]320,544[/latex] in/wk
6. [latex]{5.407\times10}^{-4}[/latex] kg/s
  1. centimeters
7. [latex]452.23[/latex] km
8. 7 lb, 11 oz
9. [latex]\approx[/latex] 54 yr, 9.5 months
10. 31.7 years old
  1. 300 feet and
  2. 91,744 cm
11. The gallon size because it is $0.02/oz.
12. [latex]125,840[/latex] ft
13. 53 days
14. Houston by 419.58 km²
15. [latex]3.73\times10^{17}[/latex] m³; [latex]3.73\times10^{20}[/latex] liters
16. 31,709.8 years old
17. 946,352.9 pages
18. 187.96 cm
19. 3 ft
20. 20.86 in
21. 25.4 kg
22. 4 times
23. 4.93 mL
24. 14.79 mL
25. 12.25 lbs, 5.56 kg
26. 160 oz
27. 4731.76 mL
28. 2.464 cc
29. 0.125 qt
30. 50000 µg
31. 2.5 cc
32. 6 tsp

Prep: Linear Graphs – Intercepts Method

1. 1. I and IV; I and III
  2. I and II; III and IV
2. 2. They lie on the y-axis.
3. 2. They lie on the x-axis.

Classwork: Intercepts Method

1. y-intercept: [latex](0, 9)[/latex]; x-intercept: [latex](\frac{9}{2}, 0)[/latex]
2. y-intercept: [latex](0, 6)[/latex]; x-intercept: [latex](-6, 0)[/latex]
3. y-intercept: [latex](0, \frac{1}{2})[/latex]; x-intercept: [latex](-3, 0)[/latex]
4. y-intercept: [latex](0, \frac{17}{5})[/latex]; x-intercept: [latex](\frac{17}{8}, 0)[/latex]
5. Answers may vary.
6. y-intercept: [latex](0, 4)[/latex]; x-intercept: none
7. y-intercept: none; x-intercept: [latex](-2, 0)[/latex]
8. Answers may vary.
1. y-intercept: [latex](0, 5)[/latex]; x-intercept: [latex](2, 0)[/latex]
2. y-intercept: [latex](0, 2)[/latex]; x-intercept: [latex](-4, 0)[/latex]
3. y-intercept: [latex](0, -1)[/latex]; x-intercept: [latex](-8, 0)[/latex]
4. y-intercept: [latex](0, \frac{1}{3})[/latex]; x-intercept: [latex](-3, 0)[/latex]
5. y-intercept: [latex](0, 4)[/latex]; x-intercept: none
6. y-intercept: none; x-intercept: [latex](-2, 0)[/latex]

Homework: Intercepts Method

1. 1. Answers may vary.
  2. Answers may vary.
  1. y-intercept: [latex](0, 8)[/latex]; x-intercept: [latex](\frac{8}{3}, 0)[/latex]
  2. y-intercept: [latex](0, -2)[/latex]; x-intercept: [latex](6, 0)[/latex]
  3. y-intercept: [latex](0, \frac{2}{3})[/latex]; x-intercept: [latex](-\frac{1}{2}, 0)[/latex]
  4. y-intercept: [latex](0, -3)[/latex]; x-intercept: none

1. 1. y-intercept: [latex](0, -2)[/latex]; x-intercept: [latex](6, 0)[/latex]
  2. y-intercept: [latex](0, -1)[/latex]; x-intercept: [latex](3, 0)[/latex]
  3. y-intercept: [latex](0, 3)[/latex]; x-intercept: [latex](9, 0)[/latex]
  4. y-intercept: none; x-intercept: [latex](4, 0)[/latex]

1. Answers may vary.
2. Discuss with a classmate.
  1. [latex](0,-6)[/latex]
  2. [latex](0,-6)[/latex]
  3. Explain.
3. Explain.
4. Explain.

Prep: Linear Graphs – Slope-Intercept Method

1. 1. [latex]y = \frac{3}{2}x + 4[/latex]
  2. [latex]y = -x + 3[/latex]
  3. [latex]y = -\frac{2}{3}x + 5[/latex]
  4. [latex]y = x - 3[/latex]
  5. [latex]y = -2x - 1[/latex]
  6. [latex]y = -\frac{1}{3}x - 1[/latex]
  7. [latex]y = 2x - 6[/latex]
  8. [latex]y = \frac{3}{4}x - 6[/latex]
  9. [latex]y = -\frac{1}{4}x + 3[/latex]
  10. [latex]y = -x - 6[/latex]
  11. [latex]y = \frac{1}{6}x - \frac{1}{3}[/latex]
  12. [latex]y = -\frac{2}{3}x + 4[/latex]

1. [latex]3[/latex]
2. [latex]-\frac12[/latex]
3. [latex]-\frac{12}7[/latex]
4. [latex]-\frac{29}{28}[/latex]
5. [latex]0[/latex]
6. Undefined
7. Discuss with classmates.

Classwork: Slope-Intercept Method

1. 1. [latex]y = \frac{3}{2}x + 4[/latex];
    [latex]m = \frac{3}{2}[/latex]; y-intercept: [latex](0, 4)[/latex]
  2. [latex]y = -x + 3[/latex];
    [latex]m = -1[/latex]; y-intercept: [latex](0, 3)[/latex]
  3. [latex]y = -\frac{2}{3}x + 5[/latex];
    [latex]m = -\frac{2}{3}[/latex]; y-intercept: [latex](0, 5)[/latex]
  4. [latex]y = 2x - 3[/latex];
    [latex]m = 2[/latex]; y-intercept: [latex](0, -3)[/latex]
  5. [latex]y = -4[/latex];
    [latex]m = 0[/latex]; y-intercept: [latex](0, -4)[/latex]
  6. [latex]x = 16[/latex];
    m is undefined; y-intercept: none
  7. [latex]y = \frac{1}{6}x - \frac{1}{3}[/latex];
    [latex]m = \frac{1}{6}[/latex]; y-intercept: [latex](0, -\frac{1}{3})[/latex]
  8. [latex]y = \frac{3}{4}x - 6[/latex];
    [latex]m = \frac{3}{4}[/latex]; y-intercept: [latex](0, -6)[/latex]
  9. Answers may vary.
  10. Many answers possible.
  1. [latex]y = -\frac{2}{3}x + 5[/latex];
    [latex]m = -\frac{2}{3}[/latex]; y-intercept: [latex](0, 5)[/latex]
  2. [latex]y = 5x + 1[/latex];
    [latex]m = 5[/latex]; y-intercept: [latex](0, 1)[/latex]
  3. [latex]y = \frac{5}{2}x - 2[/latex];
    [latex]m = \frac{5}{2}[/latex]; y-intercept: [latex](0, -2)[/latex]
  4. [latex]y = \frac{1}{2}x - \frac{4}{3}[/latex];
    [latex]m = \frac{1}{2}[/latex]; y-intercept: [latex](0, -\frac{4}{3})[/latex]
  5. [latex]y = 4x[/latex];
    x-intercept: [latex](0, 0)[/latex]; y-intercept: [latex](0, 0)[/latex]. Use the slope to find another point.
  6. Compare your answers with your classmates.

1. [latex]m = -\frac{1}{2}[/latex]
2. [latex]m = -2[/latex]
3. [latex]m = -\frac{3}{8}[/latex]
4. [latex]m = \frac{96}{35}[/latex]
5. [latex]m = 0[/latex]
6. m is undefined

Parallel and Perpendicular Lines

1. [latex]m = -\frac{2}{5}[/latex]
2. [latex]m = -\frac{2}{5}[/latex]
3. The slopes are equal;
  their graphs are parallel.
1. [latex]m = \frac{1}{3}[/latex]
2. [latex]m = -3[/latex]
3. The slopes are negative reciprocals;
  their graphs are perpendicular.

Homework: Slope-Intercept Method

1. 1. [latex]y = -\frac{12}{25}x + 12[/latex];
    [latex]m = -\frac{12}{25}[/latex]; y-intercept: [latex](0, 12)[/latex]
  2. [latex]y = \frac{1}{3}x - 3[/latex];
    [latex]m = \frac{1}{3}[/latex]; y-intercept: [latex](0, -3)[/latex]
  3. [latex]y = -x + 4[/latex];
    [latex]m = -1[/latex]; y-intercept: [latex](0, 4)[/latex]
  4. [latex]y = -\frac{1}{4}x - \frac{2}{3}[/latex];
    [latex]m = -\frac{1}{4}[/latex]; y-intercept: [latex](0, -\frac{2}{3})[/latex]
  5. [latex]y = \frac{3}{4}x - \frac{15}{2}[/latex];
    [latex]m = \frac{3}{4}[/latex]; y-intercept: [latex](0, -\frac{15}{2})[/latex]
  6. [latex]y = -3[/latex];
    [latex]m = 0[/latex]; y-intercept: [latex](0, -3)[/latex]
  1. Answers may vary.
  2. Explain.

1. 1. [latex]m = -\frac{3}{2}[/latex]; y-intercept: [latex](0, -5)[/latex]
  2. [latex]y = -\frac{1}{3}x + 3[/latex];
    [latex]m = -\frac{1}{3}[/latex]; y-intercept: [latex](0, 3)[/latex]
  3. [latex]y = \frac{1}{4}x - 3[/latex];
    [latex]m = \frac{1}{4}[/latex]; y-intercept: [latex](0, -3)[/latex]
  4. [latex]y = 2x + 3[/latex];
    [latex]m = 2[/latex]; y-intercept: [latex](0, 3)[/latex]
  5. [latex]y = -2[/latex];
    [latex]m = 0[/latex]; y-intercept: [latex](0, -2)[/latex]
  6. [latex]y = \frac{3}{4}x - \frac{15}{4}[/latex];
    [latex]m = \frac{3}{4}[/latex]; y-intercept: [latex](0, -\frac{15}{4})[/latex]

1. 1. [latex]m = -\frac{1}{3}[/latex]
  2. [latex]m = 1[/latex]
  3. [latex]m = -\frac{11}{9}[/latex]
  4. [latex]m = -\frac{12}{35}[/latex]
  5. [latex]m = -\frac{81}{170}[/latex]

1. (A) and (C) are parallel; Both (A) and (C) are perpendicular to (B)

Prep: Function Notation and Applications of Linear Functions

1. 1. [latex]-6[/latex]
  2. [latex]14[/latex]
  3. [latex]\frac{7}{10}[/latex]
  4. [latex]-\frac{13}{16}[/latex]
  5. [latex]-17[/latex]
  6. [latex]147.75[/latex]
  1. [latex]x = \frac{3}{4}[/latex]
  2. [latex]t = 14[/latex]
  3. [latex]x = \frac{13}{30}[/latex]
  4. [latex]x = -\frac{3}{2}[/latex]

1. Independent: Time (months)
  Dependent: Weight (lb)
  Rate: 4 lbs per month
2. Independent: Sales ($)
  Dependent: Salary ($)
  Rate: Not given
3. Independent: Credit hours
  Dependent: Cost ($)
  Rate: $80 per hour
4. Independent: Number of visits
  Dependent: Cost ($)
  Rate: $4.50 per visit
5. Independent: Altitude
  Dependent: Temperature
  Rate: Not given
6. Independent: Time (years)
  Dependent: Meals out
  Rate: Not given

Classwork: Function Notation & Linear Applications

1. [latex]-32[/latex], input, [latex](-3, -32)[/latex]
2. [latex]-5[/latex], input, [latex](0, -5)[/latex]
3. [latex]10[/latex], output, [latex](10, 85)[/latex]
4. [latex]9a - 5[/latex], input
5. [latex]1[/latex], input, [latex](\frac{2}{3}, 1)[/latex]
6. [latex]\frac{5}{9}[/latex], output, [latex](\frac{5}{9}, 0)[/latex]
1. [latex]4[/latex]
2. [latex]1[/latex]
3. [latex]4[/latex]
4. [latex]0[/latex]
5. [latex]-6[/latex]
6. [latex]-1[/latex]
7. [latex]-3[/latex]
8. [latex]-4[/latex]

$37.50
Answers will vary by current year.
1. 260 pounds
2. 4 pounds per month
3. 15.5 months
The y-intercept is [latex](0, 20000)[/latex] which means her salary is $20,000 at $0 in sales.
The slope is [latex]m = 0.3[/latex], which means her salary increases by $0.30 per $1.00 in sales.
1. Explain
2. Check with your neighbor
3. 128 visits
1. The temperature decreases by 3.5°F per thousand ft. gain in elevation.
2. 16.6°F
3. 7,600 feet
251 meals in 2030
Many answers are possible.
Because the rate of change is not constant
3 liters of 1% low-fat; 1.8% fat in the mixture

Homework: Function Notation & Linear Applications

1. [latex]-5[/latex], input, [latex](-3, -5)[/latex]
2. [latex]23[/latex], input, [latex](4, 23)[/latex]
3. [latex]\frac{13}{2}[/latex], output, [latex](\frac{13}{2}, 33)[/latex]
4. [latex]31[/latex], input, [latex](6, 31)[/latex]
5. [latex]\frac{15}{2}[/latex], input, [latex](\frac{1}{8}, \frac{15}{2})[/latex]
6. [latex]-\frac{7}{4}[/latex], output, [latex](-\frac{7}{4}, 0)[/latex]
7. Explain
8. Discuss.
1. [latex]f(-2) = 0[/latex]
2. [latex]f(1) = -1.5[/latex]
3. [latex]f(4) = 6[/latex]
4. [latex]f(0) = -6[/latex]
5. [latex]x = -1.9, 0.6[/latex]
6. [latex]x = -2.1, 3.4[/latex]
7. [latex]x = -1[/latex]
8. [latex]x = -2, 2, 3[/latex]
9. 66 beats
10. Answers will vary by current year.
11. 1. [latex]C(x) = 115x + 1000[/latex]
  2. [latex]C(12) = $2,380[/latex]
12. 1. $99 is the initial cost
  2. DVR costs $5.99 per month
  3. [latex]C(24) = $242.76[/latex]
13. 1. Explain
  2. Check with a classmate
  3. 29 miles
14. 1. $200
  2. $3.00
  3. 200 desserts
15. 1. [latex]m = -88.2[/latex];
    Credit card debt decreases by $88.20 per year
  2. [latex]D(x) = -88.2x + 7768[/latex]
  3. $5563
16. 14 gallons of 1% acid; 21 gallons of 2%

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