Section: 答复 - 第1章:先决条件 | 16.1 答复----第1章:先决条件 | The Way To Learn

The Way To Learn

Section outline

Section 1.2: Real Numbers
::第1.2节:实际数字

Real, Rational, Integer
::真实、合理、整数

Real, Rational
::真实, 理性

Real, Rational, Integer, Whole
::真实、合理、整数、整数

Real, Irrational
::真实的, 无理的

Real, Rational
::真实, 理性

Real, Rational
::真实, 理性

Real, Irrational
::真实的, 无理的

Real, Rational, Integer, Whole, Natural
::实际、合理、整数、整体、自然

Real, Irrational
::真实的, 无理的

Real, Rational, Integer, Whole, Natural
::实际、合理、整数、整体、自然

$\begin{align*}\frac{61}{50}, \frac{\sqrt{6}}{2}= \sqrt{1.5}, \frac{16}{13} \ (\frac{\sqrt{6}}{2} \end{align*}$ and $\begin{align*}\sqrt{1.5}\end{align*}$ are equal and between $\begin{align*}\frac{61}{50}\end{align*}$ and $\begin{align*}\frac{16}{13})\end{align*}$
::6150, 621.5, 1613 (62和1.5平等, 6150至1613平等)

$\begin{align*}\text{-}7\tfrac{1}{2}, \ \text{-}3, \ \text{-}1.5, \ 5.5, \ 7\tfrac{1}{2}\end{align*}$

$\begin{align*}\text{-}2.2, \ \text{-}0.3, \ \tfrac{9}{10}, \ \sqrt{4}\end{align*}$

$\begin{align*}\tfrac{3}{4}, \ 1, \ \sqrt{3}, \ 1.85, \ \tfrac{26}{10}\end{align*}$

$\begin{align*}a = \frac{2}{3},\end{align*}$    $\begin{align*}b = 1\frac{4}{5} = 1.8,\end{align*}$    $\begin{align*}c = 2\frac{1}{4} = 2.25,\end{align*}$    $\begin{align*}d = 3 \frac{7}{9} = 3.7\overline{7}\end{align*}$
::a=23,b=145=1.8,c=214=2.25,d=379=3.7

Section 1.3: Exponents
::第1.3节:指数

$\begin{align*}\text{-}\tfrac{1}{27}\end{align*}$

24

1

$\begin{align*}\tfrac{4}{5}\end{align*}$

-729

9

$\begin{align*}\frac{1}{x^2} + \frac{2}{xy} + \frac{1}{y^2}\end{align*}$
::1x2+2xy+1y2

$\begin{align*}\frac{64{w}^{3}{y}^{9}}{{x}^{6}{z}^{12}}\end{align*}$
::64w3y9x6z12

$\begin{align*}{a}^{2}{b}^{2}{c}^{4}{d}^{2}\end{align*}$
::a2b2c4d2 (千平方厘米)

$\begin{align*}{m}^{6}+{m}^{5}-5{m}^{2}\end{align*}$
::m6+m5-5-5平方米

$\begin{align*}{x}^{9}{y}^{6}\end{align*}$

::x9y6

$\begin{align*}{x}^{2}{y}^{10}\end{align*}$

::x2y10 x2y10

$\begin{align*}\frac{8{x}^{30}}{27{y}^{60}}\end{align*}$
::8x3027y60

$\begin{align*}5{x}^{4}\end{align*}$
::5x4 5x4

$\begin{align*}\text{-}64{x}^{7}\end{align*}$
::- 64x7 - 64x7

$\begin{align*}12{x}^{15}\end{align*}$
::12x15 12x15

$\begin{align*}{x}^{8}\end{align*}$
::x8 x8

$\begin{align*}{3}^{15}\end{align*}$

$\begin{align*}{3}^{8}\end{align*}$

$\begin{align*}{3}^{8}\end{align*}$

Section 1.4: Scientific Notation
::第1.4节:科学说明

$\begin{align*}4.2 \times {10}^{4}\end{align*}$

$\begin{align*}8.7 \times {10}^{-4}\end{align*}$

$\begin{align*}1.5064 \times {10}^{2}\end{align*}$

$\begin{align*}5.6789 \times{10}^{4}\end{align*}$

$\begin{align*}9.47 \times {10}^{-3}\end{align*}$

426,000

80,000

59,670,000,000

0.000001482

0.00764

$\begin{align*}5.19 \times {10}^{5}\end{align*}$

$\begin{align*}8.05 \times {10}^{-4}\end{align*}$

$\begin{align*}4.187 \times {10}^{12}\end{align*}$

$\begin{align*}\approx 1.392857 \times {10}^{2}\end{align*}$

$\begin{align*}3.8906125 \times {10}^{15} \ \mathrm{or} \ 3,\!890,\!612,\!500,\!000,\!000\end{align*}$
::3. 906125x1015或3 890 612 500 000 000

$\begin{align*}\approx 3.0715 \times {10}^{-13} \ \mathrm{or} \ 0.00000000000030715\end{align*}$
::=3.0715x10-13 或 0.0000000030715

Section 1.5: Radicals
::第1.5节:激进

5

$\begin{align*}2\sqrt{6}\end{align*}$

$\begin{align*}20\sqrt{5}\end{align*}$

$\begin{align*}\tfrac{1}{2}\end{align*}$

$\begin{align*}\tfrac{3}{2} \ \mathrm{or} \ 1\tfrac{1}{2}\end{align*}$
::32 或 112

0.4

0.1

3.61

9.95

1.41

44.72

0.5 (or, when set to 2 decimal places, 0.50)
::0.5(或,如果定在小数点后两位,为0.50)

1.16

0.61

0.1 (or, when set to 2 decimal places, 0.10)
::0.1(或,如果定在小数点2,小数点后为0.10)

$\begin{align*}{45}^{\frac{1}{5}} \approx 2.14\end{align*}$

$\begin{align*}140^{\frac{1}{9}} \approx 1.73\end{align*}$

$\begin{align*}{50}^{\frac{3}{8}} \approx 4.34\end{align*}$

$\begin{align*}{\sqrt[3]{72}^{5}} \approx 1,\!246.10\end{align*}$

$\begin{align*}\sqrt[4]{{125}^{3}}\approx 37.38\end{align*}$

$\begin{align*}2\sqrt{15}+4\sqrt{3}\end{align*}$

$\begin{align*}a-b\end{align*}$
::a-b (a-b)

$\begin{align*}4x+20\sqrt{x}+25\end{align*}$
::4x+20x+25

$\begin{align*}\frac{7\sqrt{15}}{15}\end{align*}$

$\begin{align*}\frac{9\sqrt{10}}{10}\end{align*}$

$\begin{align*}\frac{2\sqrt{5}}{5}\end{align*}$

16

81

32

125

243

4

$\begin{align*}\left(\frac{2}{3}\right)^{\frac{8}{4}} = \left(\frac{2}{3}\right)^{2} = \frac{4}{9}\end{align*}$

$\begin{align*}\left(\frac{7}{2}\right) ^{\frac{6}{3}} = \left(\frac{7}{2}\right) ^{2} = \frac{49}{4} \ \mathrm{or} \ 12\frac{1}{4}\end{align*}$

:7263=(722=494或1214)

$\begin{align*}{\left({16}^{\frac{1}{2}}\right)}^{\frac{6}{2}} = {16}^{\frac{6}{4}} = 64\end{align*}$

$\begin{align*}2a{b}^{2}\sqrt[3]{6b} \end{align*}$

::2ab23/6b

$\begin{align*}\frac{2x}{3y}\sqrt[3]{ \frac{2{x}^{2}}{5y} }\end{align*}$

::2x3y32x25y

False
::假假

$\begin{align*}\text{-}18\sqrt{2}\end{align*}$

$\begin{align*}7\sqrt{6}+9\sqrt{3}\end{align*}$

$\begin{align*}\text{-}26x\sqrt{2x}\end{align*}$
::- 26x%2x

$\begin{align*}7\sqrt{3a}\end{align*}$
::7_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

$\begin{align*}5x\sqrt[3]{4}\end{align*}$

::5x34

$\begin{align*}r \approx 6.098 \ cm\end{align*}$
::r r6. 098厘米

$\begin{align*}r \approx 3.0456 \ cm\end{align*}$

::r3.0456厘米

Section 1.6: Expressions with One or More Variables
::第1.6节:带有一个或多个变量的表达式

$\begin{align*}22x\end{align*}$
::22x 22x

$\begin{align*}1.35y\end{align*}$
::1.35y

$\begin{align*}\tfrac{3}{4}\end{align*}$

$\begin{align*}\tfrac{z}{4}\end{align*}$
::z 4 z4

22

21

4

-5

16

-79

$\begin{align*}\text{-}\tfrac{3}{2} \ \mathrm{or} \ \text{-}1\tfrac{1}{2}\end{align*}$

::-32或-112

$\begin{align*}\text{-}\tfrac{11}{7} \ \mathrm{or} \ \text{-}1\tfrac{4}{7}\end{align*}$
::- 117或-147

$\begin{align*}\tfrac{3}{10}\end{align*}$

-8

-53

$\begin{align*}\text{-}\tfrac{37}{91}\end{align*}$

-10

$\begin{align*}3\tfrac{1}{9} \ \mathrm{or} \ \tfrac{28}{9}\end{align*}$
::319或289

$\begin{align*}c \approx 7.85 \ inches\end{align*}$
::c$7.85英寸

$\begin{align*}A=93.5 \ square \ inches\end{align*}$
::A=93.5平方英寸

$15.84

Approximately 26.1 hours
::大约26.1小时

$\begin{align*}A= 110.25 \ square \ miles\end{align*}$
::A=110.25平方英里

Section 1.7: Factoring Polynomials
::第1.7节:保理一夫多妻制

$\begin{align*}7(x-2)\end{align*}$
::7(xx-2)

$\begin{align*}3x(1+3y)\end{align*}$
::3x(1+3y)

$\begin{align*}yz(x+y{z}^{2})\end{align*}$
::yz(x+yz2)

$\begin{align*}2(x+5)(x+3)\end{align*}$
::2(x+5)(x+3)

$\begin{align*}5(x-7)(x-7)\end{align*}$

::5(x-7)(x-7)

$\begin{align*}\text{-}x(x-7)(x-10)\end{align*}$

::-x(x--7)(x-10)

$\begin{align*}2(x-4)(x+4)({x}^{2} + 16)\end{align*}$
::2(x-4)(x+4)(x2+16)

$\begin{align*}{x}^{2}(5x - 2)(5x - 2)\end{align*}$

::x2(5x-2)(5x-2)

$\begin{align*}3x(2x+1)(2x+1)\end{align*}$
::3x( 2x+1)( 2x+1)

$\begin{align*}3(2c-5)(2c+5)\end{align*}$

::3(3)2(c)-5(2c+5)

$\begin{align*}6(x+10)(x-10)\end{align*}$
::6(xx+10) (x-10)

$\begin{align*}\text{-}5(t+2)(t+2)\end{align*}$

::-5(t+2(t+2)+2)

$\begin{align*}6(x+4)(x-1)\end{align*}$
::6(xx+4)(x-1)

$\begin{align*}\text{-}(n-3)(n-7)\end{align*}$
:n-3(n-7))

$\begin{align*}2(a+1)(a-8)\end{align*}$
::2(a+1)(a-8)

Section 1.8: Solving Multi-Step Equations
::第1.8节:解决多级数

$\begin{align*}p=15\end{align*}$
::p=15 (p=15)

$\begin{align*}j=18\frac{2}{3}\end{align*}$
::j=1823 j=1823

$\begin{align*}b=1\end{align*}$
::b=1 =1

$\begin{align*}x=4.5\end{align*}$
::x=4.5xx=4.5

$\begin{align*}x=\text{-}6\end{align*}$
::x=-6x=6

$\begin{align*}k = \tfrac{1}{6}\end{align*}$
::k=16 k=16

$\begin{align*}c = \text{-}14\end{align*}$
::c=14岁

$\begin{align*}x=4\end{align*}$
::x=4x=4

$\begin{align*}x=\tfrac{6}{5} \ \mathrm{or} \ 1\tfrac{1}{5}\end{align*}$
::x=65 或 115

$\begin{align*}t=\text{-}4\end{align*}$
::t = 4

$\begin{align*}x=\tfrac{12}{7} \ \mathrm{or} \ 1\tfrac{5}{7}\end{align*}$
::x=127或157

$\begin{align*}d = \tfrac{5}{9}\end{align*}$
::d=59

$\begin{align*}x=\text{-}1\end{align*}$
::x=-1x=-1

$\begin{align*}x=\text{-}\tfrac{6}{5} \ \mathrm{or} \ \text{-}1\tfrac{1}{5}\end{align*}$
::x=-65或-115

$\begin{align*}j=\text{-}10\end{align*}$
::jj=10 j=10

Section 1.9: Inequalities
::第1.9节:不平等

$\begin{align*}x<\text{-}3 \qquad (\text{-}\infty, \text{-}3) \end{align*}$
::x-3(- - , -3)

$\begin{align*}x\ge17 \qquad [17, \infty )\end{align*}$
::17[17, ]

$\begin{align*}x>\text{-}\tfrac{1}{12} \qquad \left(\text{-}\tfrac{1}{12}, \infty\right) \end{align*}$
::x>-112(-112, )

$\begin{align*}x \ge\text{-}75 \qquad [\text{-}75, \infty) \end{align*}$
::x- 75[- 75, ]

$\begin{align*}x>\tfrac{120}{31} \qquad \left(\tfrac{120}{31}, \infty\right) \end{align*}$
::x>12031( 12031, )

$\begin{align*}x\ge\text{-}\tfrac{7}{2} \qquad \left[\text{-}\tfrac{7}{2}, \infty\right)\end{align*}$
::x-72[-72,]

$\begin{align*}x>1 \qquad (1, \infty)\end{align*}$
::x1( 1, )

$\begin{align*}\text{-}\infty < x<\infty \qquad (\text{-}\infty, \infty ) \end{align*}$
::-

$\begin{align*}x<\text{-}14 \qquad \left\{x \ | \ x<\text{-}14 \right\}\end{align*}$
::x < 14{ x { x < 14}

$\begin{align*}x\ge 92 \qquad \left\{x \ | \ x \ge 92 \right\}\end{align*}$
::x92{x x92}

$\begin{align*}x\ge \text{-}15 \qquad \left\{x \ | \ x \ge \text{-}15 \right\}\end{align*}$
::x% - 15{ x { { { x { x { x x { x { x x { x x { x { x { x { x x { x { x x x x { x x { x x { x x { x { x { x { x { x { x { x { x { x { x { x { x { x { x { x { x { x } 15}

$\begin{align*}x\ge 1\tfrac{2}{3} \qquad \left\{x \ | \ x\ge 1\tfrac{2}{3} \right\}\end{align*}$
::x123{x x123}

$\begin{align*}x < \tfrac{10}{3} \qquad \left\{x \ | \ x < \tfrac{10}{3} \right\}\end{align*}$
::x <103{x\\ x <103}

$\begin{align*}x > \text{-}120 \qquad \left\{x \ | \ x > \text{-}120 \right\}\end{align*}$
::x- 120{x x>- 120}

$\begin{align*}x > 5 \qquad \left\{x \ | \ x > 5 \right\}\end{align*}$
::x > 5{x x> 5}

$\begin{align*}\text{-}\infty < x < \infty \qquad \left\{x \ | \ \text{-}\infty < x < \infty \right\}\end{align*}$
::{\fn黑体\fs22\bord1\shad0\3aHBE\4aH00\fscx67\fscy66\2cHFFFFFF\3cH808080}不,不,不,不 {\fn黑体\fs22\bord1\shad0\3aHBE\4aH00\fscx67\fscy66\2cHFFFFFF\3cH808080}不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不。

$\begin{align*}\left\{x \ | \ x<\text{-}1 \right\}\end{align*}$

::{x {% x <-1}

$\begin{align*}\left\{x \ | \ x>\tfrac{36}{5} \right\}\end{align*}$

::{x x>365}

$\begin{align*}\left\{x \ | \ x<\text{-}9 \right\}\end{align*}$

::{x% x<-9} {x% x<-9}

$\begin{align*}\left\{x \ | \ x>\text{-}2 \right\}\end{align*}$

::{x x>-2} {x * x >-2}

$\begin{align*}\left\{x \ | \ x\ge \text{-}\tfrac{1}{5} \right\}\end{align*}$


::{x x - 15} {x x - 15}

$\begin{align*}\left\{x \ | \ x\ge \text{-}\tfrac{11}{4} \right\}\end{align*}$

::{x x-114}

$\begin{align*}\left\{x \ | \ x<14 \right\}\end{align*}$

::{x {% x <14}

$\begin{align*}\left\{x \ | \ x \le \tfrac{1}{10} \right\}\end{align*}$

::{x x110}

$\begin{align*}\left\{x \ | \ x<\tfrac{3}{5} \right\}\end{align*}$

::{x x<35}

$\begin{align*}\left\{x \ | \ x \le \tfrac{3}{2} \right\}\end{align*}$

::{x x 32}

a) 3 times b) Finitely many
:a) 3次b) 数目有限

99

Section 1.10: Absolute Value
::第1.10节:绝对值

250

12

0.003

$\begin{align*}\tfrac{2}{5}\end{align*}$

$\begin{align*}\tfrac{1}{10}\end{align*}$

23

17

9

5

1.079

$\begin{align*}\tfrac{37}{24}\end{align*}$

$\begin{align*}u=11 \ \mathrm{or} \ u=\text{-}11\end{align*}$
::u=11或u=11

$\begin{align*}x=15 \ \mathrm{or} \ x=\text{-}5\end{align*}$
::x=15 或 x= 5

$\begin{align*}r = 3 \ \mathrm{or} \ r = \text{-}\tfrac{3}{5}\end{align*}$
::r=3或r=35

$\begin{align*}z=\text{-}\tfrac{1}{5} \ \mathrm{or} \ z = \text{-}\tfrac{11}{5}\end{align*}$
::z=15或z=-115

$\begin{align*}x=4 \ \mathrm{or} \ x=\text{-}4\end{align*}$
::x=4 或 x= 4

$\begin{align*}m=8 \ \mathrm{or} \ m=\text{-}8\end{align*}$ r--8.png" style="" width="250"/>
::m=8或 m=8

$\begin{align*}x=4 \ \mathrm{or} \ x=\text{-}8\end{align*}$
::x=4 或 x= 8

$\begin{align*}x=1 \ \mathrm{or} \ x=\text{-}\tfrac{1}{5}\end{align*}$
::x=1 或 x= 15

$\begin{align*}b=\text{-}10 \ \mathrm{or} \ b = 10\tfrac{2}{5}\end{align*}$
::b=-10或b=1025

$\begin{align*}y=0 \ \mathrm{or} \ y=\text{-}1\end{align*}$
::y=0或y=-1

$\begin{align*}x=5 \ \mathrm{or} \ x=\text{-}4.5\end{align*}$
::x=5 或 x=- 4.5

No solutions
::无解决方案

Longest length = $\begin{align*}12 \tfrac{1}{32} \ inches\end{align*}$
Shortest length = $\begin{align*}11 \tfrac{31}{32} \ inches\end{align*}$
::最短长度 = 12132英寸最短长度 = 113132英寸

20 feet
::20英尺 20英尺

$16,150

Section 1.11: Imaginary and Complex Numbers
::第1.11节:想象和复杂数字

$\begin{align*}3i\end{align*}$
::3i 3i

$\begin{align*}i\sqrt{17}\end{align*}$
::i17

$\begin{align*}4i\sqrt{2}\end{align*}$
::4i2

-12

$\begin{align*}12i\end{align*}$
::12i 12i

$\begin{align*}\text{-}4\sqrt{3}\end{align*}$

$\begin{align*}\text{-}2\sqrt{15}+11i\end{align*}$
::- 2:15+11i

$\begin{align*}0 + i\end{align*}$
::0+一

$\begin{align*}18i\end{align*}$
::18i 18i

$\begin{align*}11i\end{align*}$
::11 11i

$\begin{align*}\text{-}4i\end{align*}$
::-4i -4i

$\begin{align*}\text{-}i\end{align*}$
::- i - i

$\begin{align*}1.1i\end{align*}$
::1.11i

$\begin{align*}\text{-}i\end{align*}$
::- i - i

24

$\begin{align*}i\end{align*}$
:一) i

1

$\begin{align*}\text{-}i\end{align*}$
::- i - i

-25

-225

$\begin{align*}720i\sqrt{15}\end{align*}$
::720i15

A real number and an imaginary number

::一个真实的号码和一个想象中的号码

$\begin{align*}13-7i\end{align*}$
::13-7i 13-7i

$\begin{align*}10-\tfrac{1}{3}i\end{align*}$
::10-13i

$\begin{align*}4 + 5\sqrt{10}i\end{align*}$
::4+510i

$\begin{align*}0.27i\end{align*}$
::0.27i

$\begin{align*}3\sqrt{3} + 0.4i\end{align*}$
::33+0.4i

$\begin{align*}15+18{j}^{4}i\sqrt{2j}\end{align*}$
::15+18j4i2j

$\begin{align*}\text{-}2+2i\end{align*}$ and $\begin{align*}4-2i\end{align*}$
::-2+2i和4-2i

Section 1. 12: Coordinate Geometry
::第1.12节:协调几何

a. $\begin{align*}(5,6)\end{align*}$
b. $\begin{align*}(\text{-}5, 5)\end{align*}$
c. $\begin{align*}(\text{-}2, 3)\end{align*}$
d. $\begin{align*}(\text{-}2, \text{-}2)\end{align*}$
e. $\begin{align*}(3, \text{-}4)\end{align*}$
f. $\begin{align*}(2, \text{-}6)\end{align*}$
::a. (5,6) b. (5,6) b. (5,5,5) c. (2,3) d. (2,2) e. (3,4) f. (2,6)

$\begin{align*}(\text{-}2, 2)\end{align*}$

Quadrant I
::四方一

Quadrant II
::二次四方会议

Quadrant IV
::第四四四大四国

Quadrant III

::四方三

-1

-2

4

Undefined
::未定义

0

$\begin{align*}\text{-}\tfrac{1}{18}\end{align*}$

$\begin{align*}\text{-}\tfrac{5}{6}\end{align*}$

Parallel

::平行平行

Perpendicular

::心眼

Parallel

::平行平行

Perpendicular

::心眼

Neither

::中无

$\begin{align*}y=\text{-}5x-7\end{align*}$
::y=-5x-7 y=-5x-7

$\begin{align*}y=\tfrac{2}{3}x-5\end{align*}$
::y=23x-5

$\begin{align*}y=\tfrac{1}{4}x+2\end{align*}$
::y=14x+2 y=14x+2

$\begin{align*}y=\text{-}x-4\end{align*}$
::y=-x-4

$\begin{align*}y=\text{-}\tfrac{1}{3}x -4 \end{align*}$
::y=- 13x- 4 y=- 13x- 4

$\begin{align*}y=\text{-}\tfrac{2}{5}x+7\end{align*}$
::y=25x+7 y=25x+7

$\begin{align*}x=\text{-}1\end{align*}$
::x=-1x=-1

Section 1.13: Linear Equations
::第1.13节:线性等式

The solutions are points on the coordinate plane, as opposed to values on a number line.
::解决方案是坐标平面上的点,而不是数字线上的值。

(Table values may vary.)
$\begin{align*}\begin{array}{|c|c|} \hline x & y \\\hline 1 & \text{-}4 \\\hline 2 & \text{-}1 \\\hline 3 & 2 \\\hline \end{array}\end{align*}$

:表值可能变化。 ) xy1-42-132

Section 1.14: Intervals and Interval Notation
::第1.14节:间间和间和

$\begin{align*}[\text{-}3, 1)\end{align*}$

$\begin{align*}(0, 2)\end{align*}$

$\begin{align*}(\text{-}3, +\infty )\end{align*}$

$\begin{align*}(\text{-}\infty , 2]\end{align*}$

$\begin{align*}x >1 \end{align*}$ ∴ $\begin{align*}(1, +\infty )\end{align*}$
::x1 (1, )

$\begin{align*}x \end{align*}$ ≤ $\begin{align*}\text{-}2 \end{align*}$ ∴ $\begin{align*}(\text{-}\infty , 2]\end{align*}$

::x__-2____________________________________________________________________________________________________________________________________________________________________________________________________________________

$\begin{align*}(\text{-}\infty , \text{-}3) \ (0, +\infty )\end{align*}$

$\begin{align*}(\text{-}\infty , \text{-}5)\end{align*}$

$\begin{align*}(\text{-}3, 5]\end{align*}$

$\begin{align*}(\text{-}\infty , 2) \ (2, +\infty )\end{align*}$

$\begin{align*}Domain\!:(\text{-}4, 6) \ Range\!:(\text{-}2, 7)\end{align*}$
::域( 4, 6) 范围 2, 7)

$\begin{align*}Domain\!: (\text{-}5, 7] \ Range\!: [\text{-}1.25, 8), \ [\text{-}1, 8) \end{align*}$ is also acceptable
::范围:[-1.25,8] [1,8] 也可以接受

$\begin{align*}[\text{-}1, 3]\end{align*}$

$\begin{align*}[\text{-}2, 1)\end{align*}$

$\begin{align*}(2, 5]\end{align*}$

$\begin{align*}(\text{-}3, +\infty )\end{align*}$

Section 1.15: Average Rate of Change
::第1.15节:平均变化率

At $\begin{align*}x = 1, y = 1\end{align*}$ and at $\begin{align*}x = 3, y = 27\end{align*}$ , so the average rate of change is $\begin{align*}\frac{26}{2} = 13\end{align*}$ or $\begin{align*}\frac{13}{1}\end{align*}$ .
::x=1,y=1和x=3,y=27,平均变化率为262=13或131。

At $\begin{align*}x = \text{-}4, \ y = \text{-}64,\end{align*}$ and at $\begin{align*}x = \text{-}1, y = \text{-}1\end{align*}$ , so the average rate of change is $\begin{align*}\frac{63}{3} = 21\end{align*}$ or $\begin{align*}\frac{21}{1}\end{align*}$ .
::x=4、y=-64和x=1、y=1-1,因此平均变化率为633=21或211。

If $\begin{align*}f(1) = 2\end{align*}$ and the average rate of change of $\begin{align*}f\end{align*}$ between $\begin{align*}1\end{align*}$ and $\begin{align*}5\end{align*}$ is $\begin{align*}3\end{align*}$ , then $\begin{align*}f(2) = 5 : f(3) = 8 : f(4) = 11, \end{align*}$ and $\begin{align*}f(5) = 14\end{align*}$ .
::如果f(1)=2,1-5之间的平均变化率为3,f(2)=5:f(3)=8:f(4)=11,f(5)=14。

Jamie's average speed during the 1st half of the trip was: $\begin{align*}\frac{21km}{1.5hr}\end{align*}$ $\begin{align*}= 14 \end{align*}$ $\begin{align*}km/hr\end{align*}$ . During the last half it was $\begin{align*}\frac{15km}{1.5hr} = 10\end{align*}$ $\begin{align*}km/hr\end{align*}$ . His entire trip was $\begin{align*}\frac{36km}{3hr} = 12\end{align*}$ $\begin{align*}km / hr\end{align*}$ . Jamie averaged more than $\begin{align*}11.5 \end{align*}$ $\begin{align*}km / hr\end{align*}$ .
::杰米在行程第1半段的平均速度是:21公里1.5hr = 14公里/小时,最后一半是15公里1.5hr = 10公里/小时,整个行程是36公里3hr= 12公里/小时,平均超过11.5公里/小时。

The difference in price is $0.35 total, the time change was 5 days, therefore the gas price averaged a change of $0.07 per day.
::价格差额为0.35美元,时间变化为5天,因此天然气价格平均每天变动0.7美元。

The population difference was 1,317 over a period of 21 years. The average rate of change was $\begin{align*}\frac{1,\!317}{21\ } \approx 62.7\end{align*}$ persons per year.
::21年间的人口差异为1,317人,年平均变化率为1,31721 62.7人。

The change in price is $335 over an increase of $\begin{align*}18 \end{align*}$ $\begin{align*}{yd}^{3}.\end{align*}$ The average change in length is $\begin{align*}\frac{335}{18} = $18.61/{yd}^{3}.\end{align*}$
::价格变动为335美元,比增加18 yd3美元增加335美元。平均长度变动为33518美元=18.61/yd3美元。

The increase in length is 2 inches, the increase in weight is 4 lbs. The average change in length is $\begin{align*}\frac{2in}{4lbs} = \frac{1 in}{2 lbs} = \frac{.5 in}{1 lb}.\end{align*}$
::长度增加2英寸,重量增加4磅。平均长度变化为2英寸4磅1,平均长度变化为2英寸4=1英寸2,平均长度变化为5英寸1。

The change in speed is 15 mph, the increase in efficiency is 5 mpg. The average increase in efficiency is $\begin{align*}\frac{15mph}{5mpg} = 3\frac{mph}{mpg} \end{align*}$ or $\begin{align*}\frac{1mpg}{3mph}.\end{align*}$
::速度变化为 15 mph, 效率提高为 5 mpg。效率平均提高为 15 mph5mpg= 3 mphmpg 或 1 mpg3mph。

If $\begin{align*}y = f(x) = {x}^{2} + x + 2, \end{align*}$ then when $\begin{align*}x = \text{-}1, \ y = \text{-}2, \end{align*}$ and when $\begin{align*}x = 2, \ y = 4.\end{align*}$
a) Average rate of change: $\begin{align*}\frac{\Delta y = 6 }{\Delta x = 3 }\ = 2\end{align*}$
b) Graph of $\begin{align*}f\end{align*}$ and the graph of the line through $\begin{align*}(\text{-}1, \text{-}2) \end{align*}$ and $\begin{align*}(2, 4)\!: \end{align*}$
c) $\begin{align*}m=2\end{align*}$
d) Answers will vary, but should note that the slope is the slope of the line.
::如果y=f(x)=x2+x+2,那么当x=1,y=2和x=2,y=2,y=4。 a) 平均变化率: y=6*x=3=2b) f 和通过 (-1-2) 和(2,4): c) m=2 d 的线条图和图,答案会不同,但应指出,斜坡是线的斜坡。

a) Amy's average driving speed for the trip was $\begin{align*}42.5 mph \ \text{or} \ \frac{85 mi}{120min}\end{align*}$ .
b) Her average speed for the entire trip (including the stop at the diner) was $\begin{align*}\frac{85mi}{130min} = 39.2 mph\end{align*}$ .
::a) Amy的平均驾驶速度为42.5米或85米120min。 (b) 整个行程(包括餐厅停靠站)的平均速度为85米130min=39.2毫米。

If the weight $\begin{align*}w(t)\end{align*}$ (in grams) of tumor, $\begin{align*}t\end{align*}$ weeks after it forms is given by $\begin{align*}w(t) = \frac{{t}^{2}}{15}\end{align*}$ , then the average rate at which the tumor is growing during the 5th week after it was formed is the increase in weight "during" week 5. Subtract the weight at week 6 from the weight at week 5: $\begin{align*}\frac{36}{15} - \frac{25}{15} \approx 0.75g.\end{align*}$
::如果肿瘤的重量(吨)(克)在肿瘤形成后数周以 w(t)=t215表示,则肿瘤形成后第5周的平均生长速度是“在”第5周的重量增加。将第6周的重量从第5周的体重中减去:3615-25150.75g。

$10,833

$\begin{align*}\frac{5}{12}\end{align*}$

$200

5 mph
::5毫米 5毫米

Section 1.16: Relations and Functions
::第1.16节:关系和职能

A function is a statement defining a single result for each question, or a single output of each input.
::函数是指为每个问题确定单一结果的语句,或每个输入的单一输出。

Yes
::是是

Yes
::是是

Yes
::是是

Answers vary, but should mention how the function does not always have the same output for a given input.
::答案不尽相同,但应提及该函数对某一输入的输出并不总是相同。

Function
::函数职能职能职能职能职能职能职能职能

Not a function
::非函数函数

Not a function
::非函数函数

Function
::函数职能职能职能职能职能职能职能职能

Function
::函数职能职能职能职能职能职能职能职能

Not a function
::非函数函数

Not a function
::非函数函数

Function
::函数职能职能职能职能职能职能职能职能

Function
::函数职能职能职能职能职能职能职能职能

Yes, this is a function. One boy, one corsage/date.
::是的,这是一个函数,一个男孩,一个衣冠楚楚/日期。

It does change the answer; now it is not a function. Cory is one boy with two corsages/dates.
::它确实改变了答案; 现在它不是一个函数。 Cory 是一个男孩, 有两个套装/ 日期。

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