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