Representing the video of learning mathematics.

Representing the video of learning mathematics.
A. Solving Problem Graph Math
Problem :
13. The figure above shows the graph of . If the function h is defined by , what is the value of ?
Answer :
We are looking for

3
1
2




(substitute , in the function); for look at the graph.


So, the solution of
13. Let the function f be defined by , if . What is the value of ?
Answer :
Looking for , what is f when ?
The information is








Substitute to

So the answer of is 28.
17. In the xy-coordinate plane the graph of intersects line l at (0,p) and (5,t). What is the greatest possible value of the slope of l ?
Answer :
Looking for is greatest m


Line l




Line l :

x y
0 p
5 t

B. Factoring Polynomials
Algebraic long division
For example :
Is a factor of
make along division problem for mathematics school



- bringing down

-

-
0
no remainder
then
is a factor of

Is also a factor of
= ( )( ) can be foctor into
= ( ) , sharing the factor for the equation of
0 = ( )
Thus ever solving all equations , we get
= 0
Or

Or

The roots of are 3, -1, -2.

3 roots for this 3rd degree equation quadratic (2nd degree) equations always have at most 2 roots.
A 4th degree equation would have 4 or fewer roots and so on.
The degree of a polynomial equations always limits the number of roots.

Long division for a 3rd order polynomial =
1 Find a partial quotient of by dividing x into to get .
2 Multiply by the divisor and substract the product from the dividend.
3 Repeat the process until you either “clear it out” or reach a remainder.

Section D
Properties of polynomial graphs
Polynomial have even or odd degrees.

C. Pre-Calculus
Graph of a rational function
Can have discontinuities, because has a polynomial in denominator
For example :

When the function become
imposible
For this function choosing is a bad idea.
break in function graph
Graph
Insert x = 0

(0,-2)
Insert x = 1

that is imposible
x = 1

D.
Discontinuity







BREAK






Rational function don’t always this way
Not all rational functions will give zero in denominator.



never zero, because of the + 1


no break







Don’t forget
Rasional functions denominator can be zero!


For polynomial the graph is a smooth unbroken curve
Rational functions
x zero in thr denominator is apossible situation, there is no value for the functions so break in the graph

break 2 ways
missing point in the graph
for example
the graph like this