答复 - Ch 3: 权力、多功能和合理功能

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1. The graph of a quadratic is called a  parabola.
   ::二次曲线的图叫做抛物线。
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2. A parabola opens up if the leading coefficient is positive.
   ::如果主要系数为正数,则开启抛物线。
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3. If the coefficient of $\begin{align*}y\end{align*}$  is positive, the parabola opens right.
   ::如果y的系数是正数,则抛物线打开正确。
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4. The vertex is the extreme (lowest or highest) point of a parabola that opens up or down.
   ::顶点是向上或向下打开的抛物线的极端(最低或最高)点。
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5. The line of symmetry divides a parabola in two symmetrical parts.
   ::对称线将抛物线分为两个对称部分。
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6. The graph is a parabola with the vertex at (0, 3).
   
   ::该图是一个抛物线,顶点为(0, 3) 。
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7. The parabola opens down, with the vertex at (2, 0).
   
   ::抛物线向下打开,顶部为(2,0)。
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8. The parabola opens up, is narrower than the reference, and has a vertex at (-2, -8).
   
   ::抛物线打开,比引用范围小,在( 2 - 8) 有顶点( 2 - 8) 。
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9. a. The parabola opens down.
   b. The vertex is at (-1, 2)
   c. It is not stretched, but reflected across the $\begin{align*}x\end{align*}$ -axis and shifted left 1 and up 2.
   ::a. 抛物线向下打开。b. 顶部为(-1, 2), c. 不伸展,但反射到X轴,左转1, 上移2。
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10. $\begin{align*}y=6{x}^{2}\end{align*}$  is the narrowest because it is stretched vertically the most.
    ::y=6x2 是最窄的,因为它垂直伸展最多。
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11. $\begin{align*}y=\text{-}{x}^{2}\end{align*}$  
    
    ::y=-x2 y=-x2
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12. $\begin{align*}y=3x^2+6x+1\end{align*}$  
    
    ::y=3x2+6x+1
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13. $\begin{align*}y=\tfrac{1}{2}x^2+2x+4\end{align*}$  
    
    ::y=12x2+2x+4
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14. $\begin{align*}y=(x-3)^2+4\end{align*}$  
    
    ::y=(x-3)2+4
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15. $\begin{align*}y=\text{-}{x}^{2}-8x-17\end{align*}$  
    
    ::y=-x2-8x-17
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16. Maximum height is 11.25 yds.
    ::最大高度为11.25 yds。
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17. At max height, the ball is 15 yds down the field.
    ::在最高高度,球在球场下方15岁
18. 
    
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19. You could determine the height and distance by approximating the vertex (the highest point), knowing that the line of symmetry is halfway between 0 and 30. Thus, the vertex is about (15, 11).
    ::了解对称线介于0至30之间,可以通过接近顶点(最高点)确定顶点的高度和距离,从而确定顶点大约为15、11。

Section 3.3: Polynomial Functions
::第3.3节:多功能

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1. The real roots are -3, 2, and 3.
   
   ::真正的根是3,3,2,3
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2. The real roots are -5, -2, and 2.
   
   ::真正的根源是5 -2和2
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3. The real root is -1.
   
   
   ::真正的根是 -1
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4. The real root is 4.
   
   ::真正的根是4
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5. The real root is 1.
   
   ::真正的根是1
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6. One factor is $\begin{align*}(x-3)\end{align*}$ .
   
   ::一个因素是 (x-3) 。
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7. One factor is $\begin{align*}(x+1)\end{align*}$ .
   
   ::一个因素是 (x+1) 。
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8. Factors are $\begin{align*}(x-4)\end{align*}$ , $\begin{align*}(x+4)\end{align*}$ , and $\begin{align*}(x+2)\end{align*}$ .
   
   ::因素是(x-4)、(x+4)和(x+2)。
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9. There are no integer roots.
   
   ::没有整数根 。
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10. Factors are $\begin{align*}(x+7)\end{align*}$ , $\begin{align*}(2x+3)\end{align*}$ , and  $\begin{align*}(x-1)\end{align*}$ .
    
    ::因素是(x+7)、(2x+3)和(x-1)。
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11. Zeros: 1 and approximately -2.343, -0.471, and 1.814
    End behavior: As  $\begin{align*}x\end{align*}$  approaches ±∞,  $\begin{align*}y\end{align*}$  approaches +∞.
    Sample test  points: (-1, -4),  (0, 2),  and (1.47, -1.195)
    
    ::零: 1 和 约 -2.343,-0.471 和 1. 814 最终行为: 作为 x 接近 , y 接近 。 抽样测试点 1 - 4, (0, 2) 和 (1.47, - 1. 195)
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12. Zeros: -3 and 1
    End behavior: As  $\begin{align*}x\end{align*}$  approaches ±∞,  $\begin{align*}y\end{align*}$  approaches +∞. 
    Sample test  points: (-4, 65),  (0, -3), and (2, 35)
    
    ::零: - 3 和 1 结束行为: 当 x 接近 , y 接近 。 抽样测试点 4, 65) , (0, 3) 和 (2, 35)
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13. Zeros: -2 and approximately 2.672
    End behavior: As  $\begin{align*}x\end{align*}$  approaches ±∞,  $\begin{align*}y\end{align*}$  approaches -∞. 
    Sample test  points: (-3, -63), (0, 6), and (3, -15)
    
    ::零: - 2 和 大约 2. 672 最终行为: 当 x 接近 , y 接近 - 。 抽样测试点 3 ) - 63, (0 , 6) 和 (3 , 15)
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14. Zeros: -3, -2, -1, and 1
    End behavior: As  $\begin{align*}x\end{align*}$  approaches ±∞,  $\begin{align*}y\end{align*}$  approaches -∞. 
    Sample test  points: (-2.607, 1.383), (1.469, -0.941), and (0, 6)
    
    ::零: -3, -2, -1 和 1 结束行为: 当 x 接近 , y 接近 - 。 抽样测试点 2. 607, 1. 383), (1.469, - 0.941) 和 ( 0, 6)
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15. Zeros: There are no real zeros.
    End behavior: As  $\begin{align*}x\end{align*}$  approaches ±∞,  $\begin{align*}y\end{align*}$  approaches -∞. 
    Sample test points: (-1, -3), (0, -4), and (1, -19)
    
    ::零: 没有真正的零。 结束行为 : x 接近 , y 接近 - 。 抽样测试点 1 ) - 3 , (0 , - 4) 和 (1, -19)

Section 3.4: Synthetic Division of Polynomials
::第3.4节:多边合成科

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1. $\begin{align*}x+4\end{align*}$  
   ::x+4 x+4
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2. $\begin{align*}x+1\end{align*}$  
   ::x+1 x+1
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3. $\begin{align*}a+5\end{align*}$  
   ::a+5 +5
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4. $\begin{align*}x+2\end{align*}$  
   ::x+2 x+2
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5.   $\begin{align*}{x}^{2}+4x-1 + \frac{12}{x+2}\end{align*}$  
   ::x2+4x- 1+12x+2
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6. $\begin{align*}4{x}^{2}+17x+16\end{align*}$  
   ::4x2+17x+16
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7. $\begin{align*}2x-1 - \frac{4}{2x+1}\end{align*}$  
   ::2 - 1 - 42x+1
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8. $\begin{align*}2{x}^{3}-33{x}^{2}+267x-2,\!423+\frac{21,\!849}{x+9}\end{align*}$  
   ::2x3-33x2+267x-2,423+21,849x+9
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9. $\begin{align*}{x}^{2}+2x-1\end{align*}$  
   ::x2+2x- 1
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10. $\begin{align*}3{x}^{4}+3{x}^{3}+7{x}^{2}+7x+6+\frac{4}{x-1}\end{align*}$  
    ::3x4+3x3+7x2+7x6+6+4x-1
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11. Numbers 6 and 9 have no remainder. Having no remainder means the divisor in synthetic division is a root.
    ::第6和第9号没有剩余部分。没有剩余部分,就意味着合成部分的断层是根。
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12. $\begin{align*}(x-k)\end{align*}$  is a factor when  $\begin{align*}k\end{align*}$  is a zero.  $\begin{align*}f(k)=0\end{align*}$  if and only if  $\begin{align*}k\end{align*}$  is a zero.
    :x-k) 是指当 k 是 0 时的系数。 f(k)=0, 前提是 k 是 0 。
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13. a.  $\begin{align*}f(\text{-}2) = \text{-}14\end{align*}$  
    b. The remainder is $\begin{align*}\text{-}14\end{align*}$ , which is the same as  $\begin{align*}f(\text{-}2)\end{align*}$ . 
    ::a. f(-2)=-14 b. 其余为-14,与f(-2)相同。
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14. $\begin{align*}x = \text{-}4, \tfrac{1}{6}, \text{-}\tfrac{5}{2}\end{align*}$  
    ::x=4-4、16-52
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15. $\begin{align*}x=5, \pm \sqrt{2}\end{align*}$  
    ::x=5,%2x=5,%2
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16. $\begin{align*}x=2, \tfrac{1}{3}, \tfrac{1}{2}\end{align*}$  
    ::x=2,13,12 x=2,13,12
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17. $\begin{align*}x= \text{-}4, \text{-}4, \text{-}1, 2\end{align*}$  
    ::x=4、4、4、1、2
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18. $\begin{align*}x=\text{-}2, 0, \text{-}\tfrac{3}{2}, \tfrac{1}{3}\end{align*}$  
    ::x=-2,0,-32,13
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19. The area of the base is  $\begin{align*}x^2-5x-12.\end{align*}$  
    ::基座区域为 x2-5x-12。
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20. $\begin{align*}D = \tfrac{1}{\pi} - \tfrac{4}{\pi h}+ \tfrac{20}{\pi h^2}\end{align*}$  
    ::D=14h+20h2

Section 3.5: Real Zeros of Polynomials
::第3.5节:多元体实际零

1. $\begin{align*}\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20\end{align*}$  
2. $\begin{align*}\pm \tfrac{1}{4}, \pm \tfrac{1}{2}, \pm \tfrac{3}{4}, \pm 1, \pm \tfrac{5}{4}, \pm \tfrac{3}{2}, \pm \tfrac{5}{2}, \pm 3, \pm \tfrac{15}{4}, \pm 5, \pm \tfrac{15}{2}, \pm 15\end{align*}$  
3. $\begin{align*}\pm \frac{1}{2}, \pm 1, \pm 2, \pm 4, \pm 8\end{align*}$  
4. $\begin{align*}\pm 1, \pm 3, \pm 9\end{align*}$  
5. $\begin{align*}\pm \tfrac{1}{8}, \pm \tfrac{1}{4}, \pm \tfrac{3}{8}, \pm \tfrac{1}{2}, \pm \tfrac{3}{4}, \pm 1, \pm \tfrac{3}{2}, \pm 2, \pm 3, \pm 4, \pm 6, \pm 8, \pm 12, \pm 24\end{align*}$  
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6. $\begin{align*}x = \tfrac{1}{3}, \tfrac{1}{2}, 2\end{align*}$  
   ::x=13,12,2
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7. $\begin{align*}x= \text{-}4, \text{-}4, \text{-}1, 2\end{align*}$  
   ::x=4、4、4、1、2
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8. $\begin{align*}x= \text{-}3, \tfrac{1\pm \sqrt{2}}{4}\end{align*}$  
   ::x=3,124
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9. $\begin{align*}x= \tfrac{3}{2}; \text{other roots are complex}\end{align*}$  
   ::x=32;其他根复杂
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10. $\begin{align*}x= 5; \text{other roots are complex}\end{align*}$  
    ::x=5;其他根复杂
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11. $\begin{align*}x= \text{-}\tfrac{5}{2}, 1, \tfrac{2 \pm \sqrt{7}}{3}\end{align*}$  
    ::x=-52,1,273
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12. $\begin{align*}x= \text{-}4\pm\sqrt{3}, \text{-}3, 2, 2\end{align*}$  
    ::x=43,3,3,2,2
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13. $\begin{align*}x= \text{-}4, \text{-}4, \tfrac{3}{2}, \tfrac{3}{2}\end{align*}$  
    ::x=4、4、32、32、32
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14. $\begin{align*}x = \text{-}5, \text{-}\tfrac{1}{3}, \tfrac{1}{3}, 5\end{align*}$  
    ::x=5-5、13、13.5
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15. $\begin{align*}x= \pm \tfrac{\sqrt{21}}{3}\end{align*}$ . There are two real solutions. The other two solutions are imaginary.
    ::x213. 有两种真正的解决方案,其他两种解决方案是想象的。

Section 3.6: Fundamental Theorem of Algebra
::第3.6节:代数基本理论

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1. 
     $\begin{align*}f(x)=(x-2)^2(x-4)^3(x-1)(x-\sqrt{2}i)(x+\sqrt{2}i) \qquad \qquad \qquad \qquad \qquad \quad \ \ \ \\ = x^8-17x^7+118x^6-438x^5+984x^4-1,\!512x^3+1,\!760x^2-1,\!408x+512\end{align*}$  
   ::f(x) = (x) = (x-2) 2(x-4) 3(x-1)(x-2i)(x-2i)(x-2i)(x+2i) =x8-17x7+118x6-438x5+984x4-1,512x3+1,760x2-1,408x+512)
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2. 
     $\begin{align*}f(x) = (x-1)(x+3)^3(x+1)(x-\sqrt{3}i)(x+\sqrt{3}i) \qquad \quad \ \ \ \\ = x^7+9x^6+29x^5+45x^4+51x^3+27x^2-81x-81\end{align*}$  
   ::f(x) =(x- 1)(x+3)(x+1)(x-3i)(x-3i)(x+3i) =x7+9x6+29x5+45x4+45x4+51x3+27x2-81x-81)
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3. 
   $\begin{align*}f(x)= (x-5)^2(x+1)^2(x-2i)(x+2i) \qquad \qquad \ \ \ \\ = x^6-8x^5+10x^4+8x^3+49x^2+160x+100\end{align*}$  
   ::f(x) = (x) = (x--5) 2(x+1) 2(x-2i)(x+2i) = x6-8x5+10x4+8x3+492+160x+100
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4. 
     $\begin{align*}f(x)= (x-i)(x+i)(x-\sqrt{2}i)(x+\sqrt{2}i) \\ = x^4+3x^2+2 \qquad \ \qquad \qquad \ \ \end{align*}$
   :x)=(x-i)(x+i)(x-2i)(x+2i)=x4+3x2+2)
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5.   $\begin{align*}f(x)= (x+3)^2(x-2)(x-i)(x+i)\end{align*}$  
    Roots are  $\begin{align*}\text{-}3 \ \mathrm{(multiplicity} \ 2), 2, i, \text{-}i\end{align*}$
   ::f(x) = (x+3) 2(x-2)(x- i)(x+i) 根为 -3(多重2), 2, i, i, i
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6.   $\begin{align*}g(x)= (x-1)(x+1)(x-i)(x+i)\end{align*}$  
    Roots are  $\begin{align*}1, \text{-}1, i, \text{-}i\end{align*}$    
   ::g(x) = (x- 1) (x+1) (x-i) (x+1) (x-i) (x+i) 根为 1,-1,i,-i
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7.   $\begin{align*}h(x) = (x-4)^2(x-2)^2(x+3i)(x-3i)\end{align*}$  
    Roots are  $\begin{align*}4 \ (\mathrm{multiplicity} \ 2), 2 \ (\mathrm{multiplicity} \ 2), \text{-}3i, 3i\end{align*}$  
   ::h(x) = (x- 4) 2(x-2) 2(x+3i)(x-3i) 根为 4(多重2) 2, (多重2) , 3i, 3i
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8.   $\begin{align*}j(x)= (x-1)^2(x-3)^3(x+\sqrt{3}i)(x-\sqrt{3}i)\end{align*}$  
    Roots are  $\begin{align*}1 \ (\mathrm{multiplicity} \ 2), 3 \ (\mathrm{multiplicity} \ 3), \text{-}\sqrt{3}i, \sqrt{3}i\end{align*}$  
   :x) j(x) = (x- 1) 2(x-3) 3(x+3i)(x-3i)(x-3i) 根为 1 (多重2) , 3 (多重3), 3i, 3i
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9.   $\begin{align*}k(x)= (x-2)(x+3)(x+4)(x-1)^2\end{align*}$  
    Roots are  $\begin{align*}2, \text{-}3, \text{-}4, 1 \ (\mathrm{multiplicity} \ 2)\end{align*}$  
   ::k(x) = (x- 2) (x+3) (x+4) (x- 1) 2 根为 2, 3, 4, 1 (多重 2) 。
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10.   $\begin{align*}m(x) = (x-2)(x+2)(x-3)(x+3)(x-i)(x+i)\end{align*}$  
     Roots are  $\begin{align*}2, \text{-}2, 3, \text{-}3, i, \text{-}i\end{align*}$  
    :xx) = (x- 2) (x+2) (x- 3) (x+3) (x+3) (x- i) 根为 2, 2, 2, 3, 3, 3, i, i
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11.   $\begin{align*}n(x)= (x-6)(x+1)^3(x-\sqrt{5}i)(x+\sqrt{5}i)\end{align*}$  
     Roots are  $\begin{align*}6, \text{-}1 \ (\mathrm{multiplicity} \ 3), \sqrt{5}i, \text{-}\sqrt{5}i\end{align*}$  
    ::n(x) = (x-6)(x+1) 3 (x-5i)(x+5i) 根为 6-1 (多重 3) , 5i, 5i
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12.   $\begin{align*}p(x)= (x-2)(x+2)^3(x-\sqrt{7}i)(x+\sqrt{7}i)\end{align*}$  
     Roots are  $\begin{align*}2, \text{-}2 \ (\mathrm{multiplicity} \ 3), \sqrt{7}i, \text{-}\sqrt{7}i\end{align*}$  
    ::p(x) = (x-2)(x+2) 3(x-7i)(x+7i) 根为 2-2 (多重 3) , 7i, 7i
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13. The degree of the polynomial is the number of roots with multiplicity.
    ::多元度的程度是有多重性的根数。
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14. Multiplicity refers to a root that counts more than once, because when the polynomial is in factored form, the degree of its corresponding binomial is greater than 1.
    ::多重性是指一个不止一次的根,因为当多元性以因数形式出现时,其相应的二元性的程度大于1。
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15.   $\begin{align*}\text{-}\sqrt{3}i\end{align*}$  
    ::-3i -3i

Section 3.7: Approximating Real Zeros of Polynomial Functions
::第3.7节:多元函数接近实际零

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1. a) Leading coefficient: 3; Degree: 5
   b) 1 real zero at approximately -1.4
   c)  4 imaginary zeros
   :a) 主系数: 3; 度: 5b) 1个实际零,约1.4c) 4个假想零
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2. a) Leading coefficient: -1; Degree: 3
   b) 1 real zero at approximately 2
   c) 2 imaginary zeros
   :a) 主系数:-1;度:3b) 1实际零,约2c) 2想象零
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3. a) Leading coefficient: 1/2; Degree: 4
   b) 2 real zeros at approximately -6.3 and -1
   c) 2 imaginary zeros
   :a) 主系数:1/2; 度: 4b) 2个实际零点,约-6.3和-1c) 2个想象零
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4. a) Leading coefficient: 1; Degree: 5
   b) 5 real zeros at approximately -2.6 (multiplicity 2), -1, and 2.6 (multiplicity 2)
   c) 0 imaginary zeros
   :a) 主系数:1;第1级:5b)5个实际零点,约-2.6(多重2)、-1和2.6(多重2)、c)0个想象零
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5. a) Leading coefficient: 1; Degree: 4
   b) 4 real zeros at approximately -1 and 3 (multiplicity 3) 
   c) 0 imaginary zeros 
   :a) 主系数:1;第1级:4b)4个实际零点,大约为-1和3(多重3)c)0个想象零;
6. [-2, -1]
7. [-1, 3]
8. [-2, 4]
9. [-2, 2]
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10. The Bounded Roots Theorem is based on continuous functions, and this rational function is discontinuous at x = -3.5.
    ::断开根定理基于连续函数, 这个理性函数在 x = - 3. 5 时不连续 。
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11. [0.3125, 0.34375], Zero: 0.338
    ::[0.3125,0.34375],零:0.338
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12. [1.875, 1.9375], Zero: 1.893
    ::[1875, 1.9375], 零: 1.893

Section 3.8: Rational Functions
::第3.8节:合理职能

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1. VA: x = -4, x= -2; HA: y = 0
   ::VA: x = 4, x = - 2;HA: Y = 0
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2. VA: x = -5; SA: y = x-5
   ::VA: x = - 5; SA: y = x 5
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3. VA: x = 3; SA: y = x+3
   ::VA: x = 3; SA: y = x+3
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4. x-intercepts: (-2, 0) and (2, 0)
   ::x 拦截-2,0)和(2,0)
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5. x-intercept: (0, 0)
   ::x 拦截: (0, 0)
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6. VA: x = -3, x = 4; HA: y = 0; Intercepts: (0, -1/12), (-1, 0)
   
   ::VA: x = - 3, x = 4;HA: y = 0;拦截: (0, 1/12), (-1, 0)
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7. VA: x = 3; SA: y = x + 6; Intercepts: (0, 10/3), (2, 0), (-5, 0)
   
   ::VA: x = 3; SA: y = x + 6; 拦截: (0, 10/3), (2, 0), (5, 0)
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8. VA: x=-2; SA: y = -8x^2+8x-14 Intercepts: approximately (0.81, 0) and (0, 4)

   

   
   ::VA: x= 2; SA: y= - 8x2+8x14 截取器: 大约(0. 81, 0) 和 (0, 4)
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9. VA: x = -5/3; SA: y = 2/3x -10/6; Intercepts: (0, -2/5), (1, 0), (-1, 0)
   
   ::VA: x = - 5/3; SA: y= 2/3x - 10/6; 拦截: (0, - 2/5), (1, 0), (1, 0)
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10. VA: x = 2, x = -7; SA: y = -2x + 12 Intercepts: approximately (2.285, 0); (0, -1/7)   

    

    
    ::VA: x = 2, x = -7; SA: y = - 2x + 12 截取器: 大约 (2.285,0); (0, - 1/7)
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11. VA: x= 1/2, x= -1, x = 3; HA: y = 0; Intercepts: (0, -10), (5, 0), (-6, 0)
    
    ::VA: x= 1/2, x=-1, x = 3;HA: y = 0;拦截: (0, - 10), (5, 0), (6, 0)
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12. VA: x = 0; HA: y = 7 Intercepts: approximately (-0.87, 0), (-0.47, 0), and (1.05, 0); no y-intercept   

    

    
    ::VA:x=0;HA:y=7拦截:约(-0.87,0),(-0.47,0)和(1.05,0);无y-拦截
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13. VA: x = -6, x = 1; HA: y = 0; Intercepts: (0, -5/6), (-5/2, 0)
    
    ::VA: x = - 6, x = 1;HA: y = 0;拦截: (0,-5/6), (-5/2, 0)
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14. VA: x = 3; SA: y = -1/2x; Intercepts: (0, -2/3), (-1, 0), (4, 0)
    
    ::VA: x = 3; SA: y = - 1/2x; 拦截: (0, - 2/3), (-1, 0), (4, 0)
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15. If we divide,  $\begin{align*}\frac{3x^2-x-10}{3x+5}=x-2.\end{align*}$  This can also be found by factoring the numerator and denominator, and canceling the like factor of  $\begin{align*}3x+5\end{align*}$ . This creates a hole,  not an asymptote. 
    
    ::如果我们分隔, 3x2- x- 103x+5=x-2, 也可以通过乘以分子和分母, 并取消类似因数 3x+5 来找到。 这会造成一个洞, 而不是一个小洞 。
16. 
    

Section 3.9: Analysis of Rational Functions
::第3.9节:合理职能分析

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1.   $\begin{align*}y = \frac{(x-2)(x+5)}{x-2}\end{align*}$ ; $\begin{align*}x \ne 2\end{align*}$
   ::y= (x- 2) (x+5) x-2; x2
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2.   $\begin{align*}y = \frac{(x+6)(x-4)}{x-4}\end{align*}$ ; $\begin{align*}x\ne 4\end{align*}$  
   ::y= (x+6)(x- 4) x- 4; x4
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3.   $\begin{align*}f(x) = \frac{(x-8)(x-4)}{x-4}\end{align*}$ ; $\begin{align*}x \ne 4\end{align*}$  
   :xx) = (x-8) (x-4) x-4; x4
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4.   $\begin{align*}f(x) = \frac{(x + \tfrac{3}{4})(x+\tfrac{4}{5})}{x + \tfrac{4}{5}}\end{align*}$ ; $\begin{align*}x \ne \text{-}\tfrac{4}{5}\end{align*}$
   ::f(x) = (x+34)(x+45) x+45; x- 45
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5. $\begin{align*}y = \frac{(x+6)(x+7)}{x+7}\end{align*}$ ; $\begin{align*}x \ne \text{-}7\end{align*}$  
   ::y= (x+6)(x+7) x+7; x+7
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6. Asymptotes: VA: x = 1; SA: x^2+6x+9
   Holes: none
   Intercepts: approximately (-4.7, 0), (0, -7)
   Sketch: $\begin{align*}\frac{x^3+5x^2+3x+7}{x-1}\end{align*}$  
   
   ::微粒: VA: x = 1; SA: x2+6x+9 洞: 无拦截: 大约( 4.7, 0, 0, 7) 箭头: x3+5x2+3x+3x+7x-1
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7. Asymptotes: VA: x=0; SA: y=9x
   Holes: none
   Intercepts: none
   Sketch: $\begin{align*}\frac{(9x^2+6)}{x}\end{align*}$  
   
   ::单位数: VA: x=0; SA: y=9x洞: 无截取数: 无折叠数: (9x2+6)x
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8. Asymptotes: VA: x = -3/2; HA: y = 0
   Intercepts: (0, 1/3), there is no x-intercept
   Hole: (7, 1/17)

   

   
   ::单位数: VA: x = - 3/2; HA: y = 0 拦截: (0, 1/3), 没有 x 拦截洞: (7, 1/17)
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9. Asymptotes: VA: x = -2, x = 2; SA: y = 5x – 9
   Holes: none
   Intercepts: approximately (-0.68, 0), (0.12, 0); (0, -0.25)
   Sketch:  $\begin{align*}\frac{5x^3-9x^2-7x+1}{x^2-4}\end{align*}$
    
   ::微粒: VA: x = - 2, x = 2; SA: y = 5x - 9 孔: 无截取器: 大约( -0. 68, 0, 0, 0, 0, 0, 0. 12, 0; (0, 0,-0. 25); 缓存器: 5x3 - 9x2 - 7x+1x2 - 4)
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10. No asymptotes
    Intercepts: (0, -5), (5, 0)
    Hole (-6, -11)

    

    
    ::无空位拦截: (0, -5, (5, 0) 洞口 (6, - 11)
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11. Asymptotes: VA: x = -2; SA: y = 4x – 14
    Holes: none
    Intercepts: approximately ( -1.4, 0); (0, 7/4)
    Sketch:  $\begin{align*}\frac{4x^3+2x^2+7}{(x+2)^2}\end{align*}$  
    
    ::微粒: VA: x = - 2; SA: y = 4x - 14洞: 无截取器: 大约( -1.4, 0); (0, 7/4) 缓存器: 4x3+2x2+7( x+2) 2
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12. Asymptotes: VA: x = 2; SA: y = x + 3 
    Intercepts (0, 0), (-1, 0)
    Hole: (3, 12)

    

    
    ::微粒: VA: x = 2; SA: y = x x + 3 拦截( 0, 0, 0, 1, 0) 洞口 3, 12)
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13. Asymptotes: VA: x = 0; SA: y = -6x+8
    Holes: none
    Intercepts: approximately (1.73, 0); no y-intercept
    Sketch:  $\begin{align*}\frac{\text{-}6x^3 + 8x^2+7}{x^2}\end{align*}$  
    
    ::单位数: VA: x = 0; SA: y = - 6x+8 孔: 无截取器: 大约( 1. 73, 0 ); 没有 y 截取线: - 6x3+8x2+7x2
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14. Asymptotes: VA: none; HA: y = -5
    Holes: none
    Intercepts: no x-intercept; (0, -5/2)
    Sketch:  $\begin{align*}\frac{\text{-}5x^2-2x-5}{x^2+2}\end{align*}$  
    
    ::单位数: VA: 无; HA: y = - 5洞: 无拦截: 没有 X 拦截; (0, - 5/2) 折叠: - 5x2 - 2x - 5x2+2
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15. Asymptotes: VA: x = cubic root of 2, or approx. 1.26; HA: y = 0
    Holes: none
    Intercepts: (1 , 0); (0, 1/2)
    Sketch: $\begin{align*}\frac{x-1}{x^3-2}\end{align*}$  
    
    ::单位数: VA: x = 2 的立根或约1. 26; HA: y = 0 孔: 无截取器(1, 0); (0, 1, 1/2) 缓存器: x-1x3 - 2

Section 3.10: Polynomial and Rational Inequalities
::第3.10节:多元和合理不平等

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1. $\begin{align*}\text{-}3 \le x \le 1\end{align*}$  
   ::- 3x1
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2. $\begin{align*}x < \tfrac{1}{3} \ \mathrm{or} \ x >2\end{align*}$  
   ::x13 或 x2
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3. $\begin{align*}\text{-}\tfrac{5}{2} \le x \le \tfrac{1}{3}\end{align*}$  
   ::-52x13号
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4. $\begin{align*}x < \tfrac{1}{5} \ \mathrm{or} \ x >2\end{align*}$  
   ::x15 或 x2
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5. $\begin{align*}x < 0 \ \mathrm{or} \ x > \tfrac{1}{2}\end{align*}$  
   ::x0 或 x>12
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6. $\begin{align*}\text{-}\tfrac{1}{2} < x < 0 \ \mathrm{or} \ x > \tfrac{3}{2}\end{align*}$  
   ::-12 <x <0 或 x>32
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7. $\begin{align*}\text{-}2 < x < 0 \ \mathrm{or} \ 0<x<2\end{align*}$  
   ::-2 <x <0 或 0 <x <2
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8. $\begin{align*}\text{-}\tfrac{1}{2} \le x \le \tfrac{1}{2} \ \mathrm{or} \ x \ge2\end{align*}$  
   ::- 12x=12 或 x=2
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9. $\begin{align*}\text{-}3 < n < \text{-}1 \ \mathrm{or} \ 1 < n <2\end{align*}$  
   ::-3<n<<-1或1<n<2
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10. $\begin{align*}\text{-}3 \le n \le \text{-}2 \ \mathrm{or} \ 2 \le n < 5\end{align*}$  
    ::-n-2 或 2n<5
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11. $\begin{align*}n \le \text{-}3 \ \mathrm{or} \ \text{-}\tfrac{5}{2} \le n < \tfrac{1}{3} \ \mathrm{or} \ n \ge 3\end{align*}$  
    ::n-3 或 -52n<13 或 n3
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12. $\begin{align*}n < \text{-}\tfrac{3}{2} \ \mathrm{or} \ \text{-}\tfrac{4}{3} < n < \text{-}\tfrac{1}{2} \ \mathrm{or} \ n > \tfrac{1}{2}\end{align*}$  
    ::n <-32 或 -43 <n < 12 或 n>12
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13. $\begin{align*}0 \le t \le 36.490\end{align*}$  
    ::036.490
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14. $\begin{align*}x \le -4.567 \ \mathrm{or} \ \text{-}1.294 \le x \le 1.861\end{align*}$  
    ::x4.567 或 - 1.294x_1.861
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15. $\begin{align*}\text{-}4.667 < x < 4.044 \ \mathrm{or} \ 5.000 < x < 6.623\end{align*}$  
    ::-4.667 <x<4.044或5.000 <x<6.623
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16. $\begin{align*}y > 3x - 2, x \ne \text{-}\tfrac{2}{3}\end{align*}$  
    The graph would be as follows, with missing values anywhere  $\begin{align*}x = \text{-}\tfrac{2}{3}\end{align*}$ : 
    
    ::y>3x-2,x% 23 图表如下,在 x= 23 处缺少值 :
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17. a)  $\begin{align*}{R}_{2} < 60\end{align*}$ , so 60 ohms is the max resistance. 
    b)  20 ohms, based on how the 2nd resistor would cancel out in this equation.
    :a) R2<60,所以60 ohms是最大阻力。 (b) 20 ohms,基于第二抵抗者如何在这个方程式中取消。
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18. Width is greater than 4. 
    ::宽度大于4。