多项式的图像

学习这节课之前你应该熟悉些什么

• 当 $x\rightarrow +\infty$x, right arrow, plus, infinity,$f(x)$f, left parenthesis, x, right parenthesis趋近于?
• 当 $x\rightarrow -\infty$x, right arrow, minus, infinity,$f(x)$f, left parenthesis, x, right parenthesis趋近于?

本课内容

分析多项式函数

求出$y$y轴交点

求出$x$x-轴交点

求末端走势

绘制图像

• 当 $x\rightarrow +\infty$x, right arrow, plus, infinity, $f(x)\rightarrow +\infty$f, left parenthesis, x, right parenthesis, right arrow, plus, infinity.
• 当 $x\rightarrow -\infty$x, right arrow, minus, infinity, $f(x)\rightarrow -\infty$f, left parenthesis, x, right parenthesis, right arrow, minus, infinity.

• 图像在$(-2,0)$left parenthesis, minus, 2, comma, 0, right parenthesis点与$x$x轴接触, 因为$-2$minus, 2处的零点是偶数次幂。
• 图像在$\left(\dfrac23,0\right)$left parenthesis, start fraction, 2, divided by, 3, end fraction, comma, 0, right parenthesis点穿过$x$x-轴, 因为$\dfrac23$start fraction, 2, divided by, 3, end fraction处的零点是奇数次幂。

正与负区间

请检查你是否理解

a) $g(x)=(x+1)(x-2)(x+5)$g, left parenthesis, x, right parenthesis, equals, left parenthesis, x, plus, 1, right parenthesis, left parenthesis, x, minus, 2, right parenthesis, left parenthesis, x, plus, 5, right parenthesis的$y$y轴交点是什么?

$(0$left parenthesis, 0,

• 你的答案是
• 一个整数，例如 $6$6
• 一个最简真分数,如 $3/5$3, slash, 5
• 一个最简假分数,如 $7/4$7, slash, 4
• 一个混合带分数，例如 $1\ 3/4$1, space, 3, slash, 4
• 一个精确的十进位小数，例如$0.75$0, point, 75
• pi 的倍数, 例如 12\ \text{pi} 或 2/3\ \text{pi}$

$)$right parenthesis

检查

[我需要帮助！]

b) $g(x)=(x+1)(x-2)(x+5)$g, left parenthesis, x, right parenthesis, equals, left parenthesis, x, plus, 1, right parenthesis, left parenthesis, x, minus, 2, right parenthesis, left parenthesis, x, plus, 5, right parenthesis的图像的末端走势是什么?

选出正确答案：

选出正确答案：

• (选择 A)  

  当 $x \rightarrow +\infty$x, right arrow, plus, infinity, $g(x) \rightarrow +\infty$g, left parenthesis, x, right parenthesis, right arrow, plus, infinity, 当 $x \rightarrow -\infty$x, right arrow, minus, infinity, $g(x) \rightarrow +\infty$g, left parenthesis, x, right parenthesis, right arrow, plus, infinity.

  A

  当 $x \rightarrow +\infty$x, right arrow, plus, infinity, $g(x) \rightarrow +\infty$g, left parenthesis, x, right parenthesis, right arrow, plus, infinity, 当 $x \rightarrow -\infty$x, right arrow, minus, infinity, $g(x) \rightarrow +\infty$g, left parenthesis, x, right parenthesis, right arrow, plus, infinity.
• (选择 B)  

  当$x \rightarrow +\infty$x, right arrow, plus, infinity, $g(x) \rightarrow +\infty$g, left parenthesis, x, right parenthesis, right arrow, plus, infinity, 当 $x \rightarrow -\infty$x, right arrow, minus, infinity, $g(x) \rightarrow -\infty$g, left parenthesis, x, right parenthesis, right arrow, minus, infinity.

  B

  当$x \rightarrow +\infty$x, right arrow, plus, infinity, $g(x) \rightarrow +\infty$g, left parenthesis, x, right parenthesis, right arrow, plus, infinity, 当 $x \rightarrow -\infty$x, right arrow, minus, infinity, $g(x) \rightarrow -\infty$g, left parenthesis, x, right parenthesis, right arrow, minus, infinity.
• (选择 C)  

  当 $x \rightarrow +\infty$x, right arrow, plus, infinity, $g(x) \rightarrow -\infty$g, left parenthesis, x, right parenthesis, right arrow, minus, infinity, 当 $x \rightarrow -\infty$x, right arrow, minus, infinity, $g(x) \rightarrow +\infty$g, left parenthesis, x, right parenthesis, right arrow, plus, infinity.

  C

  当 $x \rightarrow +\infty$x, right arrow, plus, infinity, $g(x) \rightarrow -\infty$g, left parenthesis, x, right parenthesis, right arrow, minus, infinity, 当 $x \rightarrow -\infty$x, right arrow, minus, infinity, $g(x) \rightarrow +\infty$g, left parenthesis, x, right parenthesis, right arrow, plus, infinity.
• (选择 D)  

  当 $x \rightarrow +\infty$x, right arrow, plus, infinity, $g(x) \rightarrow -\infty$g, left parenthesis, x, right parenthesis, right arrow, minus, infinity, 当 $x \rightarrow -\infty$x, right arrow, minus, infinity, $g(x) \rightarrow -\infty$g, left parenthesis, x, right parenthesis, right arrow, minus, infinity.

  D

  当 $x \rightarrow +\infty$x, right arrow, plus, infinity, $g(x) \rightarrow -\infty$g, left parenthesis, x, right parenthesis, right arrow, minus, infinity, 当 $x \rightarrow -\infty$x, right arrow, minus, infinity, $g(x) \rightarrow -\infty$g, left parenthesis, x, right parenthesis, right arrow, minus, infinity.

检查

[我需要帮助！]

c) $g(x)=(x+1)(x-2)(x+5)$g, left parenthesis, x, right parenthesis, equals, left parenthesis, x, plus, 1, right parenthesis, left parenthesis, x, minus, 2, right parenthesis, left parenthesis, x, plus, 5, right parenthesis图像的$x$x-轴交点是什么?

选出正确答案：

选出正确答案：

• (选择 A)  

  $(1,0)$left parenthesis, 1, comma, 0, right parenthesis, $(-2,0)$left parenthesis, minus, 2, comma, 0, right parenthesis, 以及 $(5,0)$left parenthesis, 5, comma, 0, right parenthesis

  A

  $(1,0)$left parenthesis, 1, comma, 0, right parenthesis, $(-2,0)$left parenthesis, minus, 2, comma, 0, right parenthesis, 以及 $(5,0)$left parenthesis, 5, comma, 0, right parenthesis
• (选择 B)  

  $(-1,0)$left parenthesis, minus, 1, comma, 0, right parenthesis, $(2,0)$left parenthesis, 2, comma, 0, right parenthesis, 和 $(-5,0)$left parenthesis, minus, 5, comma, 0, right parenthesis

  B

  $(-1,0)$left parenthesis, minus, 1, comma, 0, right parenthesis, $(2,0)$left parenthesis, 2, comma, 0, right parenthesis, 和 $(-5,0)$left parenthesis, minus, 5, comma, 0, right parenthesis

检查

[我需要帮助！]

d) 以下哪个图像可能是 $g(x)=(x+1)(x-2)(x+5)$g, left parenthesis, x, right parenthesis, equals, left parenthesis, x, plus, 1, right parenthesis, left parenthesis, x, minus, 2, right parenthesis, left parenthesis, x, plus, 5, right parenthesis的图像?

选出正确答案：

选出正确答案：

• (选择 A)  

  A
• (选择 B)  

  B
• (选择 C)  

  C
• (选择 D)  

  D

检查

[我需要帮助！]