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SAT数学函数的基本概念之函数的零点

2017/5/3 16:28:12来源:互联网作者:上海新航道

摘要:

  今天小编要分想那个的是SAT数学函数的定义,快来收藏吧!

  A function f is a correspondence that associates with each element a of a set called the domain (定义域) one and only one element of a set called the range(值域).

  函数的零点

  The zeros of a function f are the values of x for which f(x)=0; they are the x-intercepts of the graph of y=f(x).

  例题1. Grace kicks a soccer ball into the air, where the height of the ball follows the function h(t) = 8t – t2. After how many seconds does the ball return to the ground?

  (A) 0

  (B) 4

  (C) 6

  (D) 8

  Solution:

  球落到地面的数学含义是h(t)=0.

  h(t) = 8t – t2=0

  t(8-t)=0

  t=0 OR t=8

  选D。

  例题2. What is a possible equation for the linear function above?

  (A) y = –10/7x – 3

  (B) y = –10/7x + 3

  (C) y =10/7x – 3

  (D) y =10/7x + 3

  Solution:

  图像中最重要的两个特征:

  (1)直线的斜率为负值;

  (2)直线与X轴和Y轴的交点均为正值。

  由此可以得到正确选项,B。

  反函数

  If f is one-to-one with domain X and range Y, then there is a function, with domain Y and range X, such that

  函数的复合Combination of functions

  The composition of f with g, written as f(g(x)) is the function obtained by replacing x wherever it occurs in f(x) by g(x). We also write for f(g(x)). The domain of is the set of all x in the domain of g for which g(x) is in the domain of f.

  例题3. If f(x) = 2x and g(x) = 5x + 1, what is g (f(c))?

  (A) 2c

  (B) 10c + 1

  (C) 10c

  (D) 20c + 2

  Solution:

  g (f(x))=5(2x)+1=10x+1

  选B。

  例题4. If f (x) = 8x + 1 and g (x) = 3x – 1, what is the value of?

  Solution:

  答案:

  奇偶函数Odd and even functions

  ODD functions:

  EVEN functions:

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