# SAT考试数学考点之函数精讲

2016-09-26 13:54

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SAT数学部分所考查的知识点，包括基础代数、数据分析&实际问题、中级代数三个部分，对于中国学生而言，这些知识点难度不大，但部分知识点考查的方式与侧重点和国内考试有些差异，需要注意。

## 函数的定义

A function f is a correspondence that associateswith each element a of a set calledthe domain (定义域) oneand 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; theyare the x-intercepts of the graph of y=f(x).

(A) 0

(B) 4

(C) 6

(D) 8

Solution:

h(t) = 8t – t2=0

t(8-t)=0

t=0 OR t=8

D

(A)y = –10/7x– 3

(B)y =–10/7x + 3

(C)y =10/7x– 3

(D)y =10/7x+ 3

Solution:

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。

#### 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Combinationof functions

The composition of f with g, written as f(g(x)) isthe function obtained by replacing xwherever 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 inthe domain of f.

(A) 2c

(B) 10c + 1

(C) 10c

(D) 20c + 2

Solution

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

B

Solution

#### 奇偶函数Oddand even functions

ODD functions:

EVEN functions:

(A)y ≥ |x –2|

(B)y ≥ |x +2|

(C)y ≤ |x –2|

(D)y ≤ |x +2|

Solution:

Solution

1

(2)

I. – 1 ≤ x ≤ 9

II. 1 ≤ x ≤ 9

III. |x – 5| ≤ 4

(A) I only

(B) II and III

(C) I and II

(D) I, II and III

Solution

(A)y

(B)2/3y

(C)1/3y

(D)

Solution:

(A)|x – 1|≤ 0.01

(B)|x – 1|≤ 0.001

(C)|x – 1|≥ 0.01

(D)|x – 1|≥ 0.001

Solution

#### 函数图像

Supposedefines any function:

1.translates k units vertically (up if k>0; down if k<0);

2.translates h units horizontally (right if h>0; left if h<0);

3.stretches (shrinks) f(x) vertically by a factor of |a| if |a|>1 (|a|<1);

4.stretches (shrinks) f(x) horizontally by a factor of if |a|>1 (|a|<1);

5. reflectsabout the x-axis. (the reflection is vertical.);

6. reflectsabout the y-axis. (the reflection is horizontal.);

(A) g(x) is greater than or equal to zero.

(B) g(x) is greater than or equal to negativeone.

(C) g(x) is greater than or equal to negativetwo.

(D) g(x) is greater than negative one, butsmaller than five.

Solution:

g(x) = f(x)– 1，图像整体向下平移一个单位，选C

(A) g(x) =2x – 5

(B)  g(x)– 3 = 2x

(C)  g(x)= 2x + 1

(D) g(x)=2x – 3

Solution

（文章内容摘选自《新SAT非官方指南》

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