函数的定义

　　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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