基础代数：函数的基本概念-函数的零点
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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