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SAT數學函數的基本概念之函數的零點

2017/5/3 16:28:12來源：互聯網作者：上海新航道

雅思/托福/國際備考寒假班

新航道雅思/托福/TOEFL Junior/.免費代報名！

新航道SAT培訓;助力SAT考試。。。

摘要：

今天小編要分想那個的是SAT數學函數的定義,快來收藏吧!

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

函數的零點

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).

例題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

(D) 8

Solution:

球落到地面的數學含義是h(t)=0.

h(t) = 8t – t2=0

t(8-t)=0

t=0 OR t=8

選D。

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

(A) y = –10/7x – 3

(B) y = –10/7x + 3

(D) y =10/7x + 3

Solution:

圖像中最重要的兩個特征：

(1)直線的斜率為負值;

(2)直線與X軸和Y軸的交點均為正值。

由此可以得到正確選項，B。

反函數

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

函數的復合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.

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

(A) 2c

(B) 10c + 1

(D) 20c + 2

Solution：

g (f(x))=5(2x)+1=10x+1

選B。

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

Solution：

答案：

奇偶函數Odd and even functions

ODD functions: