tugas englishII video pre-calculus, selasa jam ke-3

Nama: Yogawati Wulandari
Nim:07305144006
Prodi:Mat,NR
Video I
PRE-CALCULUS: GRAPH OF A RATIONAL FUNCTION
Pre – calculus, an advanced form of secondary school algebra, is a foundational mathematical dispcipline. It is sometimes considered to be an honors course. Courses and textbooks in precalculus are intended to prepare students for the study of calculus. Precalculus typically includes a review of algebra and trigonometry, as well as an introduction to exponential, logarithmic and trigonometric fungtions, vectors, complex numbers, conic sections, and analytic geometry. Equivalent college algebra and trigonometry.
A rational function is any function which can be written as the ratio of two polynomial functions. In the case of one variable, x, a rational function is a function of the form
Where P and Q are polynomial function in x and Q is not the zero polynomial. The domain of f is the set of all points x for which the denominator Q(x) is not zero.
Example:
The rational function is not defined at .
Video II
Limits by inspection
if f(x) representing rational function, for example by p(x) and q(x) representing poliynom, so to finish infinity limit dividedly numerator p(x) and denominator q(x) by the highest power of x that happened.
For example:
(1)
If the highest power of x in numerator more small than power of x in denominator, so the product from above is .
(2)
If the highest power of x in numerator and denominator is same, so the product from above is 3/2.
Video III
English Solving Problem Graph Math
Y=g(x)
Function h is defined by h(x)=g(2x)+2
The value of h(1)
h(x)=9(2x)+2
h(1)=9(2.1)+2 on curve g(x), if x=2 so y=1
=1+2=3
(13) Let the function f be defined by f(x)=x+1, if 2f(p)=20, the value of f(3p)?
Solve:
f(3p) when x=3p
f(x) = x+1
2f(p)=20
f(p)=10
f(p)=p+1=10
p=9
x=3p
x=3(9)
x=27
f(27)= 27 +1
= 28
(17) In the xy= coordinate plane, the graph of x=y+4 intersect line l at (0,p) and (5,t). what is the greathest possible valueof the slopeof l ?
Solve:
x=y-4
slope of line l =m=
x=0y=p
x=5y=t
m=
Video IV
f(p,q)=0
function y=f(x)=VLT
function
x=g(y):HLT=invertible
y=2x-1
x=0 y=-1
x=1/2 y=0
y=x
y=2x-1
2x=y+1
x=½ (y+1)
x=½y + ½
y=½y + ½
f(x)=2x-1
g(x) =½y + ½
f(g(x))=2(½y + ½)-1
=x+1-1=x
g(f(x))= ½(2x-1)+ ½
for example:
a)f(x)=3x+6 b)f(x)=27x
y=3x+6 y= 27x
f(x)=