4/10/2017 #Math 48B Sec 5.3

Rational Functions(有理数) which is no zero.

Polynomial 多项式

Domain(范围):Domain of a function y=f(x) is the set of all input variable,x,where f is well defined.

即y的取值，如是分子式的话则是分母不为0.

Example:

Find the domain of f(x)=x-3/x2-4

Domain:Denom(denomination分母项)不为0

所以x不为2，x不为-2

Domain:real x except 2 and -2

Vocabulary:

Denominator 分母

Numerator 分子

Addition/Plus 加

Subtraction 减

Multiplication 乘

Division 除

Quadrant 象限

f(x)=1/x

·As x approaches infinity,f(x) approaches 0

·This function is known as a reciprocal function(相反函数)

·This is a rational function and is undefined(无意义) at x=0

Asymptote(渐近线): goes very near but never touch it or cross it.

f(x)=1/x2

·As x approaches infinity,f(x) approaches 0

·This function is known as a reciprocal squared function(倒数的平方函数)

·This is a rational function and is undefined at x=0

Vertical Asymptote (垂直渐近线):A vertical asymptote of a function f(x) is a vertical line,x=a,that the graph of f(x) approaches but does not cross.

即x的取值，也就是Domain不包含的值（在该点无意义）。

Abbreviation(缩写):VA

Horizontal Asymptote (水平渐近线):A horizontal asymptote of a function y=f(x) is a horizontal line,y=b,that the graph of f(x) approaches as x approaches infinity.

Abbreviation:HA

To find Horizontal Asymptotes:

·Degree of numerater smaller than Degree of denominator. y=0

·Degree of numerater bigger than Degree of denominator. No horizantal asymptote.

·Degree od numerater equal to Degree of denominator. Horizontal asymptote is at ratio(比值) of leading coeffcients(首项系数).

其实就是对比一下分子和分母的最高次数（x右上角的小数字）。

小于则y=0，大于则No HA，等于则决定于分母最高次数前的系数比值。

e.g. y=x3+2/2x3-11

都是三次方（cubed），所以deg of num = deg of denom。这时就要看他们分母前的系数了，分子前为1，分母前为2。因此比值为1/2，即HA=1/2

Int为不大于number的最大整数。

e.g.Int(-3.8)=-4   Int(7.1)=7