Rational Functions(有理數(shù)) which is no zero.
Polynomial 多項式
Domain(范圍):Domain of a function y=f(x) is the set of all input variable,x,where f is well defined.
即y的取值碎罚,如是分子式的話則是分母不為0.
Example:
Find the domain of f(x)=x-3/x2-4
Domain:Denom(denomination分母項)不為0
所以x不為2改抡,x不為-2
Domain:real x except 2 and -2
Vocabulary:
Denominator 分母
Numerator 分子
Addition/Plus 加
Subtraction 減
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(相反函數(shù))
·This is a rational function and is undefined(無意義) at x=0
Asymptote(漸近線): 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(倒數(shù)的平方函數(shù))
·This is a rational function and is undefined at x=0
Vertical Asymptote (垂直漸近線):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的取值龄砰,也就是Domain不包含的值(在該點無意義)攘宙。
Abbreviation(縮寫):VA
Horizontal Asymptote (水平漸近線):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(首項系數(shù)).
其實就是對比一下分子和分母的最高次數(shù)(x右上角的小數(shù)字)。
小于則y=0燕少,大于則No HA凛剥,等于則決定于分母最高次數(shù)前的系數(shù)比值洪燥。
e.g. y=x3+2/2x3-11
都是三次方(cubed)熔恢,所以deg of num = deg of denom脐湾。這時就要看他們分母前的系數(shù)了,分子前為1绩聘,分母前為2沥割。因此比值為1/2耗啦,即HA=1/2
Int為不大于number的最大整數(shù)凿菩。
e.g.Int(-3.8)=-4 ? Int(7.1)=7