Chapter 3

ⓐ yes, yes ⓑ yes, yes

ⓐ no, no ⓑ yes, yes

ⓐ

ⓑ

ⓐ

ⓑ

x-intercept: $\left(2,0\right),$
y-intercept: $\left(0,\mathrm{-2}\right)$

x-intercept: $\left(3,0\right),$
y-intercept: $\left(0,2\right)$

x-intercept: $\left(4,0\right),$
y-intercept: $\left(0,12\right)$

x-intercept: $\left(8,0\right),$
y-intercept: $\left(0,2\right)$

$-\frac{4}{3}$

$-\frac{3}{5}$

undefined

0

$\mathrm{-1}$

10

ⓐ $m=\frac{2}{5};\left(0,\mathrm{-1}\right)$
ⓑ $m=-\frac{1}{4};\left(0,2\right)$

ⓐ $m=-\frac{4}{3};\left(0,1\right)$
ⓑ $m=-\frac{3}{2};\left(0,6\right)$

ⓐ intercepts ⓑ horizontal line ⓒ slope-intercept ⓓ vertical line

ⓐ vertical line ⓑ slope-intercept ⓒ horizontal line
ⓓ intercepts

ⓐ 50 inches
ⓑ 66 inches
ⓒ The slope, 2, means that the height, h, increases by 2 inches when the shoe size, s, increases by 1. The h-intercept means that when the shoe size is 0, the height is 50 inches.
ⓓ

ⓐ 40 degrees
ⓑ 65 degrees
ⓒ The slope, $\frac{1}{4},$ means that the temperature Fahrenheit (F) increases 1 degree when the number of chirps, n, increases by 4. The T-intercept means that when the number of chirps is 0, the temperature is 40°.
ⓓ

ⓐ $25
ⓑ $85
ⓒ The slope, 4, means that the weekly cost, C, increases by $4 when the number of pizzas sold, p, increases by 1. The C-intercept means that when the number of pizzas sold is 0, the weekly cost is $25.
ⓓ

ⓐ $35
ⓑ $170
ⓒ The slope, $1.8,$ means that the weekly cost, C, increases by $\text{\$}1.80$ when the number of invitations, n, increases by 1.
The C-intercept means that when the number of invitations is 0, the weekly cost is $35.
ⓓ

ⓐ parallel ⓑ not parallel; same line

ⓐ parallel ⓑ not parallel; same line

ⓐ parallel ⓑ parallel

ⓐ parallel ⓑ parallel

ⓐ perpendicular ⓑ not perpendicular

ⓐ perpendicular ⓑ not perpendicular

$y=\frac{2}{5}x+4$

$y=\text{−}x-3$

$y=\frac{3}{5}x+1$

$y=\frac{4}{3}x-5$

$y=-\frac{2}{5}x-1$

$y=-\frac{3}{4}x-4$

$y=8$

$y=4$

$y=\frac{1}{3}x-\frac{10}{3}$

$y=-\frac{2}{5}x-\frac{23}{5}$

$x=5$

$x=\mathrm{-4}$

$y=3x-10$

$y=\frac{1}{2}x+1$

$y=-\frac{1}{3}x+\frac{10}{3}$

$y=\mathrm{-2}x+16$

$y=\mathrm{-5}$

$y=\mathrm{-1}$

$x=\mathrm{-5}$

$x=\mathrm{-4}$

ⓐ yes ⓑ yes ⓒ yes ⓓ yes ⓔ no

ⓐ yes ⓑ yes ⓒ no ⓓ no
ⓔ yes

$y\ge \mathrm{-2}x+3$

$y\le \frac{1}{2}x-4$

$x-4y\le 8$

$3x-y\ge 6$

All points in the shaded region and on the boundary line, represent the solutions to $y>\frac{5}{2}x-4.$

All points in the shaded region, but not those on the boundary line, represent the solutions to $y<\frac{2}{3}x-5.$

All points in the shaded region, but not those on the boundary line, represent the solutions to $2x-3y<6.$

All points in the shaded region, but not those on the boundary line, represent the solutions to $2x-y>3.$

All points in the shaded region, but not those on the boundary line, represent the solutions to $y>-3x.$

All points in the shaded region and on the boundary line, represent the solutions to $y\ge \mathrm{-2}x.$

All points in the shaded region, but not those on the boundary line, represent the solutions to $y<5.$

All points in the shaded region and on the boundary line represent the solutions to $y\le \mathrm{-1}.$

ⓐ $10x+13y\ge 260$
ⓑ

ⓒ Answers will vary.

ⓐ $10x+17.5y\ge 280$
ⓑ

ⓒ Answers will vary.

ⓐ $\left\{1,2,3,4,5\right\}$
ⓑ $\left\{1,8,27,64,125\right\}$

ⓐ $\left\{1,2,3,4,5\right\}$
ⓑ $\left\{3,6,9,12,15\right\}$

ⓐ (Khanh Nguyen, kn68413), (Abigail Brown, ab56781), (Sumantha Mishal, sm32479), (Jose Hern and ez, jh47983) ⓑ {Khanh Nguyen, Abigail Brown, Sumantha Mishal, Jose Hern and ez} ⓒ {kn68413, ab56781, sm32479, jh47983}

ⓐ (Maria, November 6), (Arm and o, January 18), (Cynthia, December 8), (Kelly, March 15), (Rachel, November 6) ⓑ {Maria, Arm and o, Cynthia, Kelly, Rachel} ⓒ {November 6, January 18, December 8, March 15}

ⓐ $\left(\mathrm{-3},3\right),\left(\mathrm{-2},2\right),\left(\mathrm{-1},0\right),$
$\left(0,\mathrm{-1}\right),\left(2,\mathrm{-2}\right),\left(4,\mathrm{-4}\right)$
ⓑ $\left\{\mathrm{-3},\mathrm{-2},\mathrm{-1},0,2,4\right\}$
ⓒ $\left\{3,2,0,\mathrm{-1},\mathrm{-2},\mathrm{-4}\right\}$

ⓐ $\left(\mathrm{-3},0\right),\left(\mathrm{-3},5\right),\left(\mathrm{-3},\mathrm{-6}\right),$
$\left(\mathrm{-1},\mathrm{-2}\right),\left(1,2\right),\left(4,\mathrm{-4}\right)$
ⓑ $\left\{\mathrm{-3},\mathrm{-1},1,4\right\}$
ⓒ $\left\{\mathrm{-6},0,5,\mathrm{-2},2,\mathrm{-4}\right\}$

ⓐ Yes; $\left\{\mathrm{-3},\mathrm{-2},\mathrm{-1},0,1,2,3\right\};$
$\{\mathrm{-6},\mathrm{-4},\mathrm{-2},0,2,4,6\}$
ⓑ No; $\left\{0,2,4,8\right\};$
$\left\{\mathrm{-4},\mathrm{-2},\mathrm{-1},0,1,2,4\right\}$

ⓐ No; $\left\{0,1,8,27\right\};$
$\left\{\mathrm{-3},\mathrm{-2},\mathrm{-1},0,2,2,3\right\}$
ⓑ Yes; $\left\{7,\mathrm{-5},8,0,\mathrm{-6},\mathrm{-2},\mathrm{-1}\right\};$
$\left\{\mathrm{-3},\mathrm{-4},0,4,2,3\right\}$

ⓐ no ⓑ {NBC, HGTV, HBO} ⓒ {Ellen Degeneres Show, Law and Order, Tonight Show, Property Brothers, House Hunters, Love it or List it, Game of Thrones, True Detective, Sesame Street}

ⓐ No ⓑ {Neal, Krystal, Kelvin, George, Christa, Mike} ⓒ {123-567-4839 work, 231-378-5941 cell, 743-469-9731 cell, 567-534-2970 work, 684-369-7231 cell, 798-367-8541 cell, 639-847-6971 cell}

ⓐ yes ⓑ no ⓒ yes

ⓐ no ⓑ yes ⓒ yes

ⓐ $f\left(3\right)=22$ ⓑ $f\left(\mathrm{-1}\right)=6$ ⓒ $f(t)=3t^2-2t-1$

ⓐ $\left(2\right)=13$ ⓑ $f\left(\mathrm{-3}\right)=3$
ⓒ $f(h)=2h^2+4h-3$

ⓐ $4m^2-7$ ⓑ $4x-19$
ⓒ $x-12$

ⓐ $2k^2+1$ ⓑ $2x+3$
ⓒ $2x+4$

ⓐ t IND; N DEP ⓑ 205; the number of unread emails in Bryan’s account on the seventh day.

ⓐ t IND; N DEP ⓑ 460; the number of unread emails in Anthony’s account on the fourteenth day

ⓐ yes ⓑ no

ⓐ no ⓑ yes

The domain is $\left[\mathrm{-5},1\right].$ The range is $\left[\mathrm{-4},2\right].$

The domain is $\left[\mathrm{-2},4\right].$ The range is $\left[\mathrm{-5},3\right].$

ⓐ $f(0)=0$ ⓑ $f=\left(\frac{\pi }{2}\right)=2$ ⓒ $f=\left(\frac{\mathrm{-3}\pi }{2}\right)=2$ ⓓ $f(x)=0$ for $x=\mathrm{-2}\pi ,\text{−}\pi ,0,\pi ,2\pi$ ⓔ $(\mathrm{-2}\pi ,0),(\text{−}\pi ,0),(0,0),(\pi ,0),(2\pi ,0)$ ⓕ $(0,0)$ ⓖ $[\mathrm{-2}\pi ,2\pi ]$ ⓗ $[\mathrm{-2},2]$

ⓐ $f(0)=1$ ⓑ $f(\pi )=\mathrm{-1}$ ⓒ $f(\text{−}\pi )=\mathrm{-1}$ ⓓ $f(x)=0$ for $x=-\frac{3\pi }{2},-\frac{\pi }{2},\frac{\pi }{2},\frac{3\pi }{2}$ ⓔ $\left(\mathrm{-2}\text{pi},0\right),\left(\text{−pi},0\right),\left(0,0\right),\left(\text{pi},0\right),\left(2\text{pi},0\right)$ ⓕ $\left(0,1\right)$ ⓖ $\left[\mathrm{-2}\text{pi},2\text{pi}\right]$ ⓗ $\left[\mathrm{-1},1\right]$

ⓐ A: yes, B: no, C: yes, D: yes ⓑ A: yes, B: no, C: yes, D: yes

ⓐ A: yes, B: yes, C: yes, D: no ⓑ A: yes, B: yes, C: yes, D: no

ⓐ

ⓑ

ⓐ

ⓑ

$\left(3,0\right),\left(0,3\right)$

$\left(5,0\right),\left(0,\mathrm{-5}\right)$

$\left(5,0\right),\left(0,\mathrm{-5}\right)$

$\left(2,0\right),\left(0,6\right)$

$\left(2,0\right),\left(0,\mathrm{-8}\right)$

$\left(5,0\right),\left(0,2\right)$

Answers will vary.

Answers will vary.

$\frac{2}{5}$

$\frac{5}{4}$

$-\frac{1}{3}$

$-\frac{5}{2}$

0

undefined

$-\frac{5}{2}$

$-\frac{8}{7}$

$\frac{7}{3}$

$\mathrm{-1}$

$m=\mathrm{-7};\left(0,3\right)$

$m=\mathrm{-3};\left(0,5\right)$

$m=-\frac{3}{2};\left(0,3\right)$

$m=\frac{5}{2};\left(0,\mathrm{-3}\right)$

vertical line

slope-intercept

intercepts

intercepts

ⓐ $31
ⓑ $52
ⓒ The slope, $1.75,$ means that the payment, P, increases by $\text{\$}1.75$ when the number of units of water used, w, increases by 1. The P-intercept means that when the number units of water Tuyet used is 0, the payment is $31.
ⓓ

ⓐ $42
ⓑ $168.50
ⓒ The slope, 0.575 means that the amount he is reimbursed, R, increases by $0.575 when the number of miles driven, m, increases by 1. The R-intercept means that when the number miles driven is 0, the amount reimbursed is $42.
ⓓ

ⓐ $400
ⓑ $940
ⓒ The slope, $0.15,$ means that Cherie’s salary, S, increases by $0.15 for every $1 increase in her sales. The S-intercept means that when her sales are $0, her salary is $400.
ⓓ

ⓐ $1570
ⓑ $5690
ⓒ The slope gives the cost per guest. The slope, 28, means that the cost, C, increases by $28 when the number of guests increases by 1. The C-intercept means that if the number of guests was 0, the cost would be $450.
ⓓ

parallel

neither

parallel

perpendicular

neither

perpendicular

perpendicular

neither

parallel

Answers will vary.

Answers will vary.

$y=3x+5$

$y=\mathrm{-3}x-1$

$y=\frac{1}{5}x-5$

$y=\mathrm{-1}$

$y=3x-5$

$y=\frac{1}{2}x-3$

$y=-\frac{4}{3}x+3$

$y=\mathrm{-2}$

$y=\frac{5}{8}x-2$

$y=-\frac{3}{5}x+1$

$y=-\frac{3}{2}x+9$

$y=\mathrm{-7}x-10$

$y=5$

$y=\mathrm{-7}$

$y=\text{−}x+8$

$y=\frac{1}{4}x-\frac{13}{4}$

$y=2x+5$

$y=-\frac{7}{2}x+4$

$x=7$

$y=\mathrm{-4}$

$y=4x-2$

$y=2x-6$

$x=\mathrm{-3}$

$y=\mathrm{-2}$

$y=\frac{1}{2}x+1$

$y=-\frac{4}{3}x$

$y=-\frac{3}{2}x+5$

$y=\frac{5}{2}x$

$y=4$

$y=\mathrm{-4}$

$x=\mathrm{-2}$

$y=4$

$y=-\frac{1}{2}x+5$

$y=\frac{1}{6}x$

$y=-\frac{4}{3}x-3$

$y=-\frac{3}{4}x+1$

$x=\mathrm{-2}$

$x=\mathrm{-2}$

$y=-\frac{1}{5}x-\frac{23}{5}$

$y=\mathrm{-2}x-2$

Answers will vary.

ⓐ yes ⓑ yes ⓒ no ⓓ no ⓔ no

ⓐ no ⓑ no ⓒ yes ⓓ yes ⓔ no

ⓐ yes ⓑ no ⓒ no ⓓ no ⓔ no

$y\le 3x-4$

$y\le -\frac{1}{2}x+1$

$x+y\ge 5$

$3x-y\le 6$

ⓐ $11x+16.5y\ge 330$
ⓑ

ⓒ Answers will vary.

ⓐ $15x+10y\ge 500$
ⓑ

ⓒ Answers will vary.

Answers will vary.

ⓐ {1, 2, 3, 4, 5} ⓑ {4, 8, 12, 16, 20}

ⓐ {1, 5, 7, −2} ⓑ {7, 3, 9, −3, 8}

ⓐ (Rebecca, January 18), (Jennifer, April 1), (John, January 18), (Hector, June 23), (Luis, February 15), (Ebony, April 7), (Raphael, November 6), (Meredith, August 19), (Karen, August 19), (Joseph, July 30)
ⓑ {Rebecca, Jennifer, John, Hector, Luis, Ebony, Raphael, Meredith, Karen, Joseph}
ⓒ {January 18, April 1, June 23, February 15, April 7, November 6, August 19, July 30}

ⓐ (+100, 17. 2), (110, 18.9), (120, 20.6), (130, 22.3), (140, 24.0), (150, 25.7), (160, 27.5) ⓑ {+100, 110, 120, 130, 140, 150, 160,} ⓒ {17.2, 18.9, 20.6, 22.3, 24.0, 25.7, 27.5}

ⓐ (2, 3), (4, −3), (−2, −1), (−3, 4), (4, −1), (0, −3) ⓑ {−3, −2, 0, 2, 4}
ⓒ {−3, −1, 3, 4}

ⓐ (1, 4), (1, −4), (−1, 4), (−1, −4), (0, 3), (0, −3) ⓑ {−1, 0, 1} ⓒ {−4, −3, 3,4}

ⓐ yes ⓑ {−3, −2, −1, 0, 1, 2, 3} ⓒ {9, 4, 1, 0}

ⓐ yes ⓑ {−3, −2, −1, 0, 1, 2, 3} ⓒ 0, 1, 8, 27}

ⓐ yes ⓑ {−3, −2, −1, 0, 1, 2, 3} ⓒ {0, 1, 2, 3}

ⓐ no ⓑ {Jenny, R and y, Dennis, Emily, Raul} ⓒ {RHern and ez@state.edu, JKim@gmail.com, Raul@gmail.com, ESmith@state.edu, DBroen@aol.com, jenny@aol.cvom, R and y@gmail.com}

ⓐ yes ⓑ yes ⓒ no

ⓐ yes ⓑ no ⓒ yes

ⓐ $f\left(2\right)=7$ ⓑ $f\left(\mathrm{-1}\right)=\mathrm{-8}$ ⓒ $f\left(a\right)=5a-3$

ⓐ $f\left(2\right)=\mathrm{-6}$ ⓑ $f\left(\mathrm{-1}\right)=6$ ⓒ $f\left(a\right)=\mathrm{-4}a+2$

ⓐ $f\left(2\right)=5$ ⓑ $f\left(\mathrm{-1}\right)=5$
ⓒ $f(a)=a^2-a+3$

ⓐ $f\left(2\right)=9$ ⓑ $f\left(\mathrm{-1}\right)=6$
ⓒ $f(a)=2a^2-a+3$

ⓐ $g(h^2)=2h^2+1$
ⓑ $g\left(x+2\right)=2x+5$
ⓒ $g\left(x\right)+g\left(2\right)=2x+6$

ⓐ $g(h^2)=\mathrm{-3}{h}^2-2$
ⓑ $g\left(x+2\right)=\mathrm{-3}x-8$
ⓒ $g\left(x\right)+g\left(2\right)=\mathrm{-3}x-10$

ⓐ $g(h^2)=3-h^2$
ⓑ $g\left(x+2\right)=1-x$
ⓒ $g\left(x\right)+g\left(2\right)=4-x$

2

6

22

4

ⓐ t IND; N DEP
ⓑ $N\left(4\right)=165$ the number of unwatched shows in Sylvia’s DVR at the fourth week.

ⓐ x IND; C DEP
ⓑ $N\left(0\right)=1500$ the daily cost if no books are printed
ⓒ $N\left(1000\right)=4750$ the daily cost of printing 1000 books

ⓐ no ⓑ yes

ⓐ no ⓑ yes

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

ⓐ

ⓑ D:(-∞,∞), R:{5}

ⓐ

ⓑ D:(-∞,∞), R: $\left\{\mathrm{-3}\right\}$

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

ⓐ

ⓑ D:(-∞,∞), R:[0,∞)

ⓐ

ⓑ (-∞,∞), R:(-∞,0]

ⓐ

ⓑ (-∞,∞), R:[-∞,0)

ⓐ

ⓑ (-∞,∞), R:[$\mathrm{-1},$ ∞)

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

ⓐ

ⓑ D:(-∞,∞), R:(-∞,∞)

ⓐ

ⓑ D:[0,∞), R:[0,∞)

ⓐ

ⓑ D:[1,∞), R:[0,∞)

ⓐ

ⓑ D:[ $\mathrm{-1},$ ∞), R:[−∞,∞)

ⓐ

ⓑ D:(-∞,∞), R:[1,∞)

D: [2,∞), R: [0,∞)

D: (-∞,∞), R: [4,∞)

D: $\left[\mathrm{-2},2\right],$ R: [0, 2]

ⓐ $f\left(0\right)=0$ ⓑ $\left(\text{pi}\text{/}2\right)=\mathrm{-1}$
ⓒ $f\left(\mathrm{-3}\text{pi}\text{/}2\right)=\mathrm{-1}$ ⓓ $f\left(x\right)=0$ for $x=\mathrm{-2}\text{pi},\text{−}\text{pi},0,\text{pi},2\text{pi}$
ⓔ $\left(\mathrm{-2}\text{pi},0\right),\left(\text{−}\text{pi},0\right),$ $\left(0,0\right),\left(\text{pi},0\right),\left(2\text{pi},0\right)$ $\left(f\right)\left(0,0\right)$
ⓖ $\left[\mathrm{-2}\text{pi},2\text{pi}\right]$ ⓗ $\left[\mathrm{-1},1\right]$

ⓐ $f\left(0\right)=\mathrm{-6}$ ⓑ $f\left(\mathrm{-3}\right)=3$ ⓒ $f\left(3\right)=3$ ⓓ $f\left(x\right)=0$ for no x ⓔ none ⓕ $y=6$ ⓖ $\left[\mathrm{-3},3\right]$
ⓗ $\left[\mathrm{-3},6\right]$

ⓑ, ⓒ

$(0,3)(3,0)$

$(6,0),(0,3)$

$(16,0),(0,\mathrm{-12})$