Task of English II

I.Title : Pre Calculus
Sub title : Graphs of a rational function
We can have discontinuity polynomial in denominator.
For example : ,
if , we get undefinition
if we get (0,)
We know that not all rational function will give zero in the denominator. But a rational function can be zero in the denominator.
There are 2 ways of break, they are :
i). Missing point is a loophole . we can see from the factor top and bottom.
For example : we can simplified it become
y=(x+6)
but, if we choose x=4, we can get
ii). X approaches zero inthe denominator.
II.Determining limits by inspection.
There are two rules, e.g. :
X goes to positive or negative infinity
Limits involves a polynomial divided by a polynomial
The tips are :
Looking the power of x in the numerator and the denominator.
The polynomial must be divided by a polynomial
If the power of the numaretor is higher than the denominator, so the limits is positive or negative infinity.
For example :
, the example means that a polynomial over polynomial and x approaches infinity. The highest power of x in numerator is 3, and the highest power of x in denominator is 2.
, the example has same power of the numerator and the denominator, so we can solve the question by divide the coefficient of of the numerator and the denominator. So,
III. Solving problem about graph math
There is a function , if the function h is defined by
Answer :
= 1+2
= 3
Let the function f be defined by , if
Answer : we can analog with a function f when
f(x)=x+1→2f(p)=20
f(p)=10
if x=p, we get f(p)=p+1
10=p+1
9=p
p=9 →x=9
x=3p
x=27
So,
In the xy-coordinate plane, the graph of intersects line at and what is the greatest possible value of slope of line ?
Answer :
Line :
=
0
5
p
t