Section: 答案 - Ch 9:合理函数 | 14.9 答复-第9章:合理功能

Section outline

Section 9.2 Simplifying Rational Expressions
::第9.2节简化合理表达式

Review
::回顾

$\begin{align*}\frac{4{x}^{2}}{2x+3}\end{align*}$
::422x+3

$\begin{align*}\frac{\left(x+2\right)}{x\left(x+5\right)}\end{align*}$
:x+2)xx(x+5)

$\begin{align*}\frac{\left(x-3\right)}{\left(x-4\right)}\end{align*}$
:x-3)(x-4)

$\begin{align*}\frac{\left(x+7\right)}{x\left(x-7\right)}\end{align*}$
:x+7)x(x-7)

$\begin{align*}\frac{\text{-}2\left(2x+1\right)}{\left(2x+3\right)}\end{align*}$
::-2(2x+1)(2x+3)

$\begin{align*}\frac{2(x-4)}{3(x+1)(x-1)}\end{align*}$
::2(x-4)3(x+1)(x-1)

$\begin{align*}\frac{\left(3x+4\right)}{\left(3x+1\right)}\end{align*}$
:3x+4)(3x+1)

$\begin{align*}\frac{\left(x+2\right)}{x}\end{align*}$
:x+2)x

$\begin{align*}\frac{x\left(x+3\right)\left(2x-7\right)}{4\left(x-7\right)}\end{align*}$
:xx+3)(2x-7)4(x-7)

$\begin{align*}x-2\end{align*}$
::x-2

$\begin{align*}\frac{(3x-1)}{({x}^{2}+1)}\end{align*}$
:3x-1)(x2+1)

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

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::探索更多

No, they are not the same, because $\begin{align*}\frac{x-2}{x-3}\end{align*}$ is in simplest form. $\begin{align*}\frac{5x}{10x}\end{align*}$ can be reduced using division rules, so it does simplify to $\begin{align*}\frac{1}{2}\end{align*}$ .
::不,它们不同,因为 x-2x-3 的形式最简单。 5x10x 可以通过分法规则减少,因此简化为12。

Width: Perimeter = 1:6
::宽度:周边=1:6

Base: Perimeter = 2:5
::基数:周边=2:5

$\begin{align*}2(x+1)(x-1)=2{x}^{2}-2\end{align*}$
::2(x+1)(x-1)=2x2-2

You can't cancel the $\begin{align*}{x}^{2};\end{align*}$ you have to factor the polynomials before simplifying.
::您无法取消 x2 ; 在简化前, 您必须先将多义因素考虑在内。

Section 9.3 Multiplying and Dividing Rational Expressions
::第9.3节乘数和分裂性合理表达式

Review
::回顾

$\begin{align*}{x}^{5}{y}^{8}\end{align*}$
::x5y8

$\begin{align*}\frac{{x}^{2}+5x-3}{2{x}^{2}-3x+1}\end{align*}$
::x2+5x - 32x2 - 3x+1

$\begin{align*}\frac{2\left({x}^{2}+14x-15\right)}{\left(8{x}^{2}-18x+9\right)}\end{align*}$
::2(x2+14x-15)(8x2-18x+9)

$\begin{align*}\frac{2x-3}{x-3}\end{align*}$
::2 - 3x-3 - 3

$\begin{align*}\frac{8y{z}^{5}}{7x}\end{align*}$
::8yz57x 8yz57x

$\begin{align*}\frac{x({x}^{2}+6x+2)}{\text{-}3\left(6{x}^{2}-13x-5\right)}\end{align*}$
::x(x2+6x+2)-3(6x2-13x-5)

$\begin{align*}\frac{x\left(x+2\right)}{\left(x+3\right)}\end{align*}$
::x( xx+2)( x+3)

$\begin{align*}\frac{\left(x+5\right)}{\left(5x+3\right)}\end{align*}$
:x+5)(5x+3)

$\begin{align*}\frac{2}{3x(x-3)}\end{align*}$
::23x(x-3)

$\begin{align*}\frac{x}{5(x+3)}\end{align*}$
::x5( x+3 )

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

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

$\begin{align*}\frac{\left(2{x}^{2}-3x-12\right)\left(x-3\right)}{3\left({x}^{2}+4x-7\right)}\end{align*}$
:2x2-3x-12)(x-3)3 (x2+4x-7)

$\begin{align*}\frac{2\left({x}^{2}+2x+15\right)}{\left(8{x}^{2}-3x+15\right)}\end{align*}$
::2(x2+2x+15)(8x2-3x+15)

$\begin{align*}\frac{\left(x+1\right)\left(4{x}^{2}+5x-8\right)}{\left(x+2\right)\left(-{x}^{2}+6x+1\right)}\end{align*}$
:x+1)(4x2+5x-8)(x+2)(-x2+6x+1)

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::探索更多

Error is that 4 and x are not common factors. The correct answer is

$\begin{align*}\frac{(x + 4)\cancel{(x - 4)}}{\cancel{(x - 4)}} = (x + 4).\end{align*}$
::错误是 4 和 x 不是常见系数。正确的答案是 (x+4)(x-4)(x-4)(x-4) = (x+4) = (x+4)。

$\begin{align*}{R}_{1}=\frac{{R}_{2}{R}_{TOT}}{{R}_{2}-{R}_{TOT}};{R}_{2}=\frac{{R}_{1}{R}_{TOT}}{{R}_{1}-{R}_{TOT}}\end{align*}$
::R1=R2RTOTR2-RTOT;R2=R1RTOTR1-RTOT

$\begin{align*}\frac{x-1}{x+4}\end{align*}$
::x-1x+4 x-1x+4

1. False, you add the exponents. 2.True. 3. True. 4. False. The answer is $\begin{align*}{x}^{2}+4x+4\end{align*}$ .
::1. 假,您添加前言。 2. true. 3. true. 4. false, 答案为 x2+4x+4。

a. $\begin{align*}\frac{3y}{10x}\end{align*}$ b. $\begin{align*}\frac{6{z}^{4}}{5{y}^{2}}\end{align*}$ c. $\begin{align*}\frac{1}{x(x-1)}\end{align*}$
::a. 3y10x b. 6z45y2 c. 1x(x-1)

No. To get the same answer, you need to have $\begin{align*}\frac{1\div 1}{2\div 6}\end{align*}$ .
::不,要得到同样的答案,你需要 1126。

1. $\begin{align*}2+\frac{1}{1+\frac{1}{2+\frac{2}{4+\frac{4}{5}}}};2+\frac{1}{1+\frac{1}{2+\frac{2}{5+\frac{5}{6}}}}.\end{align*}$ 2. $\begin{align*}2.667,2.723,2.717,2.707,2.700.\end{align*}$ 3. As the number of terms increases, the number comes close to 2.7. 4. $\begin{align*}2+\frac{1}{1+\frac{1}{2+\frac{2}{6+\frac{6}{7}}}}\end{align*}$ . Yes, the decimal value is 2.696.
::1. 2+11+12+12+24+45;2+11+12+12+25+56。 2.2.667、2.723、2.717、2.707、2.700。 3. 随着用语数目的增加,数目接近2.7.4. 2+11+12+12+26+67。是,小数点值为2.696。

Section 9.4 Adding and Subtracting Rational Expressions with Like Denominators
::第9.4节添加和减减与类似引号相同的逻辑表达式

Review
::回顾

$\begin{align*}\frac{7}{x}\end{align*}$
::7x 7x

$\begin{align*}\frac{6}{x}\end{align*}$
::6x 6x

$\begin{align*}\frac{9-2x}{5x}\end{align*}$
::9-2x5x

$\begin{align*}\frac{4+x}{x}\end{align*}$
::4+xxx 4+xx

1

$\begin{align*}\frac{x+5}{x-2}\end{align*}$
::x+5x-2

4

$\begin{align*}\frac{5x+11}{(x-5)(x+1)}\end{align*}$
::5x+11(x-5)(x+1)

$\begin{align*}\frac{3}{x+2}\end{align*}$
::3x+2 3x+2

$\begin{align*}\frac{{x}^{2}+2x+4}{{x}^{3}-8}\end{align*}$
::x2+2x+4x3-8

$\begin{align*}\frac{2(x+1)}{{x}^{2}+1}\end{align*}$
::2(x+1)x2+1

$\begin{align*}\frac{20{x}^{2}-20x-7}{(2x+1)(2x-3)(2x+3)}\end{align*}$
::20x2-20x-7(2x+1)(2x-3)(2x+3)

$\begin{align*}\frac{3({x}^{2}-2x-12)}{(x+4)(x-4)(x-2)}\end{align*}$
::3(x2-2x-12)(x+4)(x-4)(x-2)

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::探索更多

You need a common denominator of 15.
::你需要一个共同的15分之一的分母。

When simplifying in the 1st step, there should be a + x in the numerator, not a - x .
::当第1步简化时,分子中应有一个+x,而不是一个 -x。

When simplifying in the 1st step, you should have $\begin{align*}2{x}^{2}+8x\end{align*}$ in the numerator.
::在第一步简化时,分子中应包含 2x2+8x 。

9 feet
::9英尺9英尺

$\begin{align*}x=\frac{6}{5};y=\frac{3}{20}\end{align*}$
::x=65;y=320

$\begin{align*}\frac{2x+5}{x+2}\end{align*}$
::2x+5x+2

Section 9.5 Adding and Subtracting Rational Expressions with Unlike Denominators
::第9.5节增加和减减与不同控号的逻辑表达式

Review
::回顾

$\begin{align*}x-3\end{align*}$
::x-33 个

No LCD
::无液晶

$\begin{align*}\frac{7}{4x}\end{align*}$
::74x 74x

$\begin{align*}\frac{{x}^{2}+3x-1}{x(x+3)}\end{align*}$
::x2+3x- 1x( x+3)

$\begin{align*}\frac{(x+10)(x-1)}{4x(x+2)}\end{align*}$
:x+10)(x-1)4x(x+2)

$\begin{align*}\frac{5}{x+2}\end{align*}$
::5x+2 5x+2

$\begin{align*}\frac{\text{-}1(x - 50}{2x^2 - 7x - 15}\end{align*}$
::-1(x- 502x2-7x-15)

$\begin{align*}\frac{2(5x-9)}{(x+2)(3x-5)}\end{align*}$
::2(5x-9)(x+2)(3x-5)

$\begin{align*}\frac{(x-3)}{2(2x-3)}\end{align*}$
:x-33)(2-2x-3-3)

$\begin{align*}\frac{3}{x-3}\end{align*}$
::3x-3

$\begin{align*}\frac{4}{x+3}\end{align*}$
::4x+3 4x+3

$\begin{align*}\frac{2(2{x}^{2}+5x+6)}{(x+5)(x+2)(x+3)}\end{align*}$
::2( 2x2+5x+6)(x+5)(x+2)(x+3)

$\begin{align*}\frac{x^2 +30x+23}{x(x-2)(3x+5)}\end{align*}$
::x2+30x+23x(x-2)(3x+5)

$\begin{align*}\frac{20{x}^{2}+42x-7}{5x(x+1)(x-1)}\end{align*}$
::20x2+42x-75x(x+1)(x-1)

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::探索更多

You need to use LCD to make the denominators the same.
::您需要使用液晶显示器使分母相同。

$\begin{align*}\frac{5x-1}{{x}^{2}-x-2}\end{align*}$
::5x-1x2-x-2

$\begin{align*}\frac{2{x}^{2}+22x-33}{2(x+3)(x-2)}\end{align*}$
::2x2+22x-32(x+3)(x-2)

Section 9.6 Solving Rational Equations Using the Least Common Denominator
::第9.6节利用最不常见数字符号解决合理等式

Review
::回顾

Yes
::是是

No
::否无

$\begin{align*}x=\text{-}5;x=2\end{align*}$
::x=-5;x=2

$\begin{align*}x=\text{-}\frac{7}{13}\end{align*}$
::x=-713 x=-713

$\begin{align*}x=\frac{1}{4}\end{align*}$
::x=14x=14

$\begin{align*}x=\frac{2}{3}\end{align*}$
::x=23x=23

$\begin{align*}x=\text{-}5;x=2\end{align*}$
::x=-5;x=2

$\begin{align*}x = \frac{3}{4}(5 + \sqrt{17}), \text{-}\frac{3}{4}(\sqrt{17} -5)\end{align*}$
::x=34(517),-34(17)-5)

$\begin{align*}x=\text{-}28;x=0\end{align*}$
::x=- 28;x=0

$\begin{align*}x=5;x=\text{-}3\end{align*}$
::x=5;x=3 x=3

$\begin{align*}x=\text{-}\frac{1}{4}\end{align*}$
::x=-14

$\begin{align*}x=\frac{\text{-}7\pm \sqrt{5}}{2}\end{align*}$
::x=-7=52

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::探索更多

$\begin{align*}x=\frac{2\sqrt{15}}{15}\end{align*}$
::x=21515

MN=10; YZ = 3
::MN=10;YZ=3

360 defective phones
::360台有缺陷电话

1,290 students
::1 290名学生

1.25 mph
::1.25 百万平方厘米

Bus speed = 35mph. Train speed =105 mph.
::班车速度=35米,火车速度=105米。

Section 9.7 Solving Rational Equations Using Cross Multiplication
::第9.7节利用交叉乘法解决合理等式

Review
::回顾

Yes
::是是

$\begin{align*}x=6,x=\text{-}2\end{align*}$
::x=6,x=2 x=6,x=2

$\begin{align*}x=\text{-}5,x=2\end{align*}$
::x=5,x=2 x=5,x=2

$\begin{align*}x=6,x=\text{-}1\end{align*}$
::x=6,x=-1

$\begin{align*}x=\pm 1\end{align*}$
::x1

$\begin{align*}x=\text{-}4,x=\frac{1}{2}\end{align*}$
::x=4,x=12 x=4,x=12

$\begin{align*}x=\text{-}3\end{align*}$
::x=-3x=3

$\begin{align*}x=\text{-}2, \frac{9}{2}\end{align*}$
::x=-2,92x=-2,92

$\begin{align*}x=\frac{5}{28}\end{align*}$
::x=528x=528

$\begin{align*}x=\text{-}40\end{align*}$
::x=-40

$\begin{align*}x=8,x=\text{-}1\end{align*}$
::x=8,x=-1

Explore More
::探索更多

a. $\begin{align*}x\neq \pm a\end{align*}$ ; b. $\begin{align*}x\neq a\end{align*}$
::a. xa;b. xa

$\begin{align*}x=21\end{align*}$
::x=21x=21

12 pages
::12页

25 ounces
::25 盎司

20 ounces
::20 盎司

160 feet
::160英尺

29.75 miles
::29.75英里

Section 9.8 Graphing Rational Functions in Standard Form
::第9.8节标准表格中的逻辑函数图示

Review
::回顾

$\begin{align*}x=\text{-}8,y=\text{-}3\end{align*}$
::x=8,y=3 x=8,y=3

$\begin{align*}x=4,y=6\end{align*}$
::x=4,y=6 x=4,y=6

Domain: $\begin{align*}\{x∈ℜ:x\neq 0\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ:y\neq 0\};\end{align*}$ Asymptotes: $\begin{align*}x=0,y=0;\end{align*}$ No intercepts.

::域 : {xR:x0}; 范围 : {yR:y0}; 微粒: x=0,y=0; 没有拦截。

Domain: $\begin{align*}\{x∈ℜ:x\neq 0\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ:y\neq 6\};\end{align*}$ Asymptotes: $\begin{align*}x=0,y=6;\end{align*}$ Intercept at x = $\begin{align*}\text{-}\frac{1}{6}\end{align*}$ .

::域 : {xR:x0} ; 范围 : {yR:y6} ; 微粒 : x= 0. y=6; 拦截 : x = - 16 。

Domain: $\begin{align*}\{x∈ℜ:x\neq 0\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ:y\neq 0\};\end{align*}$ Asymptotes: $\begin{align*}x=0,y=0\end{align*}$ ; No intercepts.

::域 : {xR:x0}; 范围 : {yR:y0}; 微粒: x=0,y=0; 没有拦截。

Domain: $\begin{align*}\{x∈ℜ:x\neq \text{-}3\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ:y\neq 0\};\end{align*}$ Asymptotes: $\begin{align*}x=\text{-}3,y=0;\end{align*}$ Intercept: $\begin{align*}(0,\text{-}\frac{1}{3})\end{align*}$ .

::域 : {xR:x_ 3}; 范围 :{yR:y0}; 微粒: x= 3,y=0; 拦截: (0, 13) 。

Domain: $\begin{align*}\{x∈ℜ:x\neq \text{-}5\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ:y\neq 0\};\end{align*}$ Asymptotes: $\begin{align*}x=\text{-}5,y=0\end{align*}$ ; Intercept: $\begin{align*}(0,\frac{1}{5})\end{align*}$ .

::域 : {xR:x* 5}; 范围 : {yR:y0}; 微粒: x= 5,y=0; 拦截: (0, 15) 。

Domain: $\begin{align*}\{x∈ℜ:x\neq 3\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ:y\neq \text{-}4\};\end{align*}$ Asymptotes: $\begin{align*}x=3,y=\text{-}4;\end{align*}$ Intercepts: $\begin{align*}(3\frac{1}{4},0),(0,\text{-}4\frac{1}{3})\end{align*}$ .

::域 : {xR:x3}; 范围 :{yR:y4}; 微粒: x=3,y=4; 截取 : (314,0,413) 。

Domain: $\begin{align*}\{x∈ℜ:x\neq \text{-}4\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ:y\neq \text{-}3\};\end{align*}$ Asymptotes: $\begin{align*}x=\text{-}4,y=\text{-}3;\end{align*}$ Intercepts: $\begin{align*}\left(\text{-}3\frac{1}{3},0\right),\left(0,\text{-}2\frac{1}{2}\right).\end{align*}$

::域 : {xR:x_ 4}; 范围 :{yR:y- 3}; 亚星点 : x= 4,y=-3; 拦截313,0, 212) (313,0, 212) 。

Domain: $\begin{align*}\{x∈ℜ:x\neq 0\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ:y\neq 2\};\end{align*}$ Asymptotes: $\begin{align*}x=0,y=2;\end{align*}$ Intercept: $\begin{align*}(\text{-}2.5,0)\end{align*}$ .

::域 : {xR:x0}; 范围 :{yR:y2}; 微粒: x=0,y=2; 拦截- 2.5,0) 。

Domain: $\begin{align*}\{x∈ℜ:x\neq \text{-}2\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ:y\neq 3\};\end{align*}$ Asymptotes: $\begin{align*}x=\text{-}2,y=3;\end{align*}$ Intercepts: $\begin{align*}(\text{-}1\frac{2}{3},0),(0,\frac{5}{2})\end{align*}$ .

::域 : {xR:x_2}; 范围 :{yR:y3}; 微粒: x=-2,y=3; 拦截-123,0,(0,52)) 。

$\begin{align*}y=\frac{1}{x-6}-4\end{align*}$
::y=1x-6 - 4

$\begin{align*}y=\text{-}\frac{1}{x+1}+3\end{align*}$
::y=-1x+1+3 y=-1x+1+3

Explore More

$\begin{align*}y=\frac{1}{x-5}+3\end{align*}$
::y=1x-5+3 y=1x-5+3

$\begin{align*}y=\frac{1}{x+3}-2\end{align*}$
::y=1x+3-2

As the volume goes down, the pressure goes up. This shows the inverse proportionality. This graph shows a rational expression with a vertical asymptote at $\begin{align*}x=0,\end{align*}$ and a horizontal asymptote at $\begin{align*}y=0\end{align*}$ .

::随着音量下降, 压力会上升。这显示了反比例性。此图显示了一种合理表达式, 以 x=0 的垂直小数表示, 以 y=0 的横向小数表示。

Section 9.9 Graphing Other Rational Functions
::第9.9节其他合理职能图示

Review
::回顾

$\begin{align*}x=\text{-}7,y=1\end{align*}$
::x=-7,y=1

$\begin{align*}x=\text{-}2,x=\text{-}4,y=0\end{align*}$
::x=-2,x=4,y=0

$\begin{align*}x=\text{-}5\end{align*}$ ; oblique asymptote: $\begin{align*}y=x-5\end{align*}$
::x= 5; 斜线渐变: y=x- 5

$\begin{align*}x=3\end{align*}$ ; oblique asymptote: $\begin{align*}y=x+3\end{align*}$
::x=3; 斜线无症状: y=x+3

Domain: $\begin{align*}\{x∈ℜ:x\neq 5\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ:y\neq 1\};\end{align*}$ Asymptotes: $\begin{align*}x=5,y=1;\end{align*}$ Intercepts: $\begin{align*}(\text{-}3,0),(0,\text{-}\frac{3}{5});\end{align*}$ Holes: none.

::域 : {xR:x5}; 范围 :{yR:y1}; 亚星点 : x=5,y=1; 拦截 3) -0, (0, 35) ; 空洞: 无。

Domain: $\begin{align*}\{x∈ℜ:x\neq \text{-}5\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ:y\neq \frac{\text{-}1}{2}\};\end{align*}$ Asymptotes : $\begin{align*}x=\text{-}5,y=\text{-}\frac{1}{2};\end{align*}$ Intercepts: $\begin{align*}(3,0),(0,\frac{3}{10});\end{align*}$ Holes: none.

::域 : {xR:x* 5}; 范围 :{yR:y* 12}; 微粒 :x= 5,y= 12; 截取 : (3,0,0,310); 空: 无。

Domain: $\begin{align*}\{x∈ℜ:x\neq -3,x\neq 4\};\end{align*}$ Range: $\begin{align*}y \in\end{align*}$ ℜ; Asymptotes: $\begin{align*}x=\text{-}3.x=4,y=0;\end{align*}$ Intercepts: $\begin{align*}(\text{-}1,0),(0,\text{-}\frac{1}{12});\end{align*}$ Holes: none.

::域 : {xR:x3,x4}; 范围 : yR; 亚本托斯: x=-3.x=4,y=0; 截取器 1- 0, (0)-112); 无空 : 无空。

Domain: $\begin{align*}\{x∈ℜ:x\neq \text{-}1.5,x\neq7\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ:y\neq 0\};\end{align*}$ Asymptotes: $\begin{align*}x=\text{-}\frac{3}{2},y=0\end{align*}$ ; Intercepts: $\begin{align*}(0,\frac{1}{3})\end{align*}$ ; Holes: $\begin{align*}x=7\end{align*}$ .

::域 : {xR:x- 1.5,x7}; 范围 :{yR:y0}; 亚星点数: x=-32,y=0; 拦截器: (0,13); 空洞: x=7。

Domain: $\begin{align*}\{x∈ℜ:x\neq 6,x\neq2\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ:y\neq 1\};\end{align*}$ Asymptotes: $\begin{align*}x=6,x=2,y=1;\end{align*}$ Intercepts: $\begin{align*}(\text{-}3,0),(\text{-}2,0),(0,\frac{1}{2});\end{align*}$ Holes: none.

::域 : {xR:x6,x2}; 范围 :{yR:y1}; 亚辛托斯: x=6,x=2,y=1; 拦截( 3, 3,0, (2,0, 0, 12); 空洞: 无。

Domain: $\begin{align*}\{x∈ℜ:x\neq -1.5,x\neq1\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ:y\neq \frac{1}{2}\};\end{align*}$ Asymptotes: $\begin{align*}x=1,x=\text{-}\frac{3}{2},y=\frac{1}{2};\end{align*}$ Intercepts: $\begin{align*}(0,\text{-}\frac{4}{3})\end{align*}$ ; Holes: none.

::域 : {xR:x1.5,x1}; 范围 :{yR:y12}; 微粒: x=1,x=-32,y=12; 拦截0)-43); 空: 无。

Domain: $\begin{align*}\{x∈ℜ:x\neq \text{-}\frac{4}{3},\text{-}2\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ:y\neq \frac{2}{3}\};\end{align*}$ Asymptotes: $\begin{align*}x=\text{-}\frac{4}{3},y=\frac{2}{3};\end{align*}$ Intercepts: $\begin{align*}(\frac{5}{2},0),(0,\text{-}\frac{5}{4});\end{align*}$ Holes: $\begin{align*}(\text{-}2,\frac{9}{2}).\end{align*}$

::域 : {xR:x- 43,-2}; 范围 :{yR:y23}; 微粒: x=-43,y=23; 拦截52,0,0,-54); 洞穴-2,92) 。

Domain: $\begin{align*}\{x∈ℜ:x\neq \text{-}5,x\neq2\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ:y\neq 1\};\end{align*}$ Asymptotes: $\begin{align*}x=\text{-}5,y=1\end{align*}$ ; Intercepts: $\begin{align*}(\text{-}2,0),(0,\frac{2}{5});\end{align*}$ Holes: $\begin{align*}(2, \frac{4}{7})\end{align*}$ .

::域 : {xR:x 5,x2}; 范围 :{yR:y1}; 微粒: x= 5,y=1; 拦截 2- 20, (0, 25); 洞口 2, 47) 。

Domain: $\begin{align*}\{x∈ℜ:x\neq \text{-}6\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ\};\end{align*}$ Intercepts: $\begin{align*}(5,0),(0,\text{-}5);\end{align*}$ Holes: $\begin{align*}(\text{-}6,1).\end{align*}$

::域 : {xR:x 6}; 范围 :{yR}; 拦截5, 5,0, 5); 洞6, 1) 。

Domain: $\begin{align*}\{x∈ℜ:x\neq 2.x\neq3\};\end{align*}$ Range: $\begin{align*}\{y∈ℜ\};\end{align*}$ Asymptotes: $\begin{align*}x=2,x=3,y=x+3\end{align*}$ ; Intercepts: $\begin{align*}(\text{-}1,0),(0,0);\end{align*}$ Holes: $\begin{align*}(3,12).\end{align*}$

::域 : {xR:x2.x3}; 范围 :{yR}; 亚速特: x=2,x=3,y=3,y=x+3; 截取( 1,0,0,0); 空 3, 12) ; 截取( 1,0,0); 空 3, 12) 。

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False, because there could be a hole.
::假的,因为可能有一个洞。

False; it will be y = 0.
::假的;它会是y=0。

None, because $\begin{align*}x^2+2\ne0\end{align*}$ for any x .
::无, 因为 x2+2+% 0 代表任何 x 。

There is a hole at $\begin{align*}x=\text{-}\frac{5}{3}\end{align*}$ .

::x=-53处有一个洞。

Darnell, because $\begin{align*}x^4-16 = (x-2)(x+2) (x^2 +4),\end{align*}$ the latter of which is never zero.
::达内尔, 因为 x4 - 16=(x-2)(x+2)(x2+4), 后者从不为零。

Zeb
::扎布

The rabbit population approaches a maximum at 200 rabbits.

::兔子数量最多接近200只兔子。

The concentration peaks at $\begin{align*}t=1,\end{align*}$ then decreases to close to zero, since the horizontal asymptote is $\begin{align*}y=0\end{align*}$ .

::浓度峰值在 t=1 时为峰值,然后降至接近于零,因为水平单点为 y=0 。

Section 9.10 Connections: Getting the Job Done
::第9.10节连接:完成任务

Teenager: 5 hours, 20 min. Father: 16 hours.
::青少年:5小时20分钟,父亲:16小时。

2 hours, 55 minutes
::2小时55分

4 hours, 48 minutes
::4小时48分48分

1 hour, 48 minutes
::1小时48分

17.14 min
::17.14分钟

Section 9.11 Connections: "Say Cheese," Great Camera Phone Photos
::第9.11节连接:“说起司”,大相机电话照片

Answers will vary depending on the phone used.
::答复将因使用的电话而异。

Answers will vary depending on the phone used in Question 1.
::答复将因问题1中使用的电话而异。

Section outline

Section 9.2 Simplifying Rational Expressions ::第9.2节 简化合理表达式

Section 9.3 Multiplying and Dividing Rational Expressions ::第9.3节 乘数和分裂性合理表达式

Section 9.4 Adding and Subtracting Rational Expressions with Like Denominators ::第9.4节 添加和减减与类似引号相同的逻辑表达式

Section 9.5 Adding and Subtracting Rational Expressions with Unlike Denominators ::第9.5节 增加和减减与不同控号的逻辑表达式

Section 9.6 Solving Rational Equations Using the Least Common Denominator ::第9.6节 利用最不常见数字符号解决合理等式

Section 9.7 Solving Rational Equations Using Cross Multiplication ::第9.7节 利用交叉乘法解决合理等式

Section 9.8 Graphing Rational Functions in Standard Form ::第9.8节 标准表格中的逻辑函数图示

Section 9.9 Graphing Other Rational Functions ::第9.9节 其他合理职能图示

Section 9.10 Connections: Getting the Job Done ::第9.10节 连接:完成任务

Section 9.11 Connections: "Say Cheese," Great Camera Phone Photos ::第9.11节 连接:“说起司”,大相机电话照片

Section 9.2 Simplifying Rational Expressions
::第9.2节简化合理表达式

Section 9.3 Multiplying and Dividing Rational Expressions
::第9.3节乘数和分裂性合理表达式

Section 9.4 Adding and Subtracting Rational Expressions with Like Denominators
::第9.4节添加和减减与类似引号相同的逻辑表达式

Section 9.5 Adding and Subtracting Rational Expressions with Unlike Denominators
::第9.5节增加和减减与不同控号的逻辑表达式

Section 9.6 Solving Rational Equations Using the Least Common Denominator
::第9.6节利用最不常见数字符号解决合理等式

Section 9.7 Solving Rational Equations Using Cross Multiplication
::第9.7节利用交叉乘法解决合理等式

Section 9.8 Graphing Rational Functions in Standard Form
::第9.8节标准表格中的逻辑函数图示

Section 9.9 Graphing Other Rational Functions
::第9.9节其他合理职能图示

Section 9.10 Connections: Getting the Job Done
::第9.10节连接:完成任务

Section 9.11 Connections: "Say Cheese," Great Camera Phone Photos
::第9.11节连接:“说起司”,大相机电话照片