AP微积分函数考点分享 据说这6大知识点很重要哦

在AP微积分的学习中，函数这一节的内容有点多，有些是同学们早就接触过的。但是同学们还是需要重头来学熊。下面来给大家讲讲AP微积分函数考点的内容吧！

• 函数的定义、函数的图像、分段函数、绝对值函数、定义域和值域等；

• 函数的运算及复合函数，函数图像的对称性；

• x的n次幂的函数、反比例函数、多项式函数、有理函数、三角函数的定义、性质和图像分析；
  

• 反函数和反三角函数的图像和性质；
  

• 指数函数和对数函数；
  

• 参数方程（只是Calculus BC所要求的内容）

函数的基本知识

1.1. Definition

If a variable y depends on a variable x in such a way that each value of x determines exactly one value of y, then we say that y is a function of x.

1.2. The vertical line test:

A curve in the xy-plane is the graph of some function f if and only if no vertical line intersects the curve more than once.

1.3. The absolute value function

函数的运算

2.1. Composition of f with g

Given functions f and g, the composition of f with g, denoted by f ο g, is the function defined by（f 。g）（x）=f（g（x））

The donation of f o g is defined to consist of all x in the domain of g for which g(x) is in the domain of f.

2.2. Symmetry Tests

a) A plane curve is symmetric about the y-axis if and only if replacing x by –x in its equation produces an equivalent equation.

b) A plane curve is symmetric about the x-axis if and only if replacing y by –y in its equation produces an equivalent equation.

c) A plane curve is symmetric about the origin if and only if replacing x by –x and y by –y in its equation produces an equivalent equation

常见的函数

3.1. Inverse function

A variable is said to be inversely proportional to a variable x if there is a positive constant k, called the constant of proportionality, such that,

3.2. Polynomials

A polynomial in x is a function that is expressible as a sum of finitely many terms of the form cxn, wherec is a constant and n is a nonnegative integar.

3.3. Rational function

A function that can be expressed as a ratio of two polynomials is called a rational function.

反函数

4.1. Inverse function

If the function f and g satisfy the two conditions：

g(f(x))=x for every x in the domain of f

f(g(x))=y for every y in the domain of g

then we say that f is an inverse of g and g is an inverse of f or that f and g are inverse functions.

4.2. The Horizontal Line Test

A function has an inverse function if and only if its graph is cut at most once by any horizontal line.

指数函数、对数函数

5.1. A function of the form f(x)=bx, where b>0, is called an exponential function with base b.

5.2. The basic characteristic of exponential function

5.3. The basic characteristic of logarithmic function

5.4. If b>0 and b≠1, then bx and logbx are inverse functions.

参数方程

6.1. Definition

Suppose that a particle moves along a curve C in the xy-plane in such a way that its x- and y- coordinates, as functions of time, arex=f(t), y=g(t)

We call these the parametric equations of motion for the particle and refer to C as the trajectory of the particle or the graphs of the equations. The variable t is called the parameter for the equations.

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AP微积分真题讲解 赶紧来收下这份最好的微积分复习资料吧

AP微积分真题讲解 赶紧来收下这份最好的微积分复习资料吧

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