project in mathematics. functions
DESCRIPTION
all about functions :)TRANSCRIPT
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Project in Math
Submitted by: Nikka Verone C. BacongonSubmitted to: Sir Cadiz
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1ST QUARTER
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Evaluating FunctionsGiven:f(x)=3x+2f(2)=3(2)+2 =6+2 =8
Substitute 2 in the given equation.
The value of x=2
Another example!The value of x=3
Given: f(x)=2x+6
=2(3)+6=6+6
f(x)=12
The value of x=a+1 f(x)=3x+2
=3(a+1)+2
=3a+3+2
=3a+5
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Inverse FunctionConsider the function f(x) = 2x + 1.
We know how to evaluate f at 3, f(3) = 23 + 1 = 7. In this section it helps to think of f as transforming a 3 into a 7
f(x)=x+3 y=x+3 x=y+3
Example: y=2x+5 x=2y+5
x-5=y2
f-1(x)=
f(x)=6-2X=6y-2X+2=6y6 6
f-1 (x)=x+2=y6
f(x)=2x3
(x )=(2y)33
3x=2y
2 2
f-1 (x)=3x=y2
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2ND QUARTER
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SYNTHETIC DIVISION
2x8-6x2+11x-6
2 -6 11 -64 -4 14
2 -2 7 8 r.
+2
X-2
Add
2x2-2x+7+ 8X-2
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2x4+3x2+4x-36
X+2
The exponent should be in order, if one is gone add
0x with the missing exponent
2x4+0x3+3x2+4x-36
X+2Now you can divide it.
2 0 3 4 36 -4 8 -22 36
2 -4 11 -18 0
2x3-4x2+11x-18
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Exponetial FunctionGiven:
25 ½ = (52) ½
=51
=5
Another example!
Transpose it.
16 3/2
(2 4) 3/2
2 12/2
2 6 = 64
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3RD QUARTER
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Logarithm FunctionBefore solving logarithm you need to arrange it first.
Example:
Log 7 x=0
7 0=x log x 8 =3
X 3=8
After arranging you can solve for the log .
Log 7 x=0
7 0=xX=1
log x 8 =3X 3=8X 3 =2 3
X=2
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LAW OF LOGARITHM
log 2 32 log2 (8)(4)
logb MN
log2 8+log2 43+2
=5 Transpose 8 & 4 using 2
logb m n log3 9 = log3 27
3 log 3 27 – log 3 3= 3-1
=2
logb MP = p logb M log3 81 4 = 4 log3 81= 4(4)
=16
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4TH QUARTER
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PARTS OF A CIRCLE
Center Point
Radius
Diameter
Chord
Tangent
Point of tangency
Secant
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RADIAN DEGREE
r= πd180o
Degree to Radian
Example
150o π
180o
Cancel the degreesAnd find the GCF of the Given numbers.
150 π
18030
5 π6
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Radian to Degrees
Example:
5 π12
The value of Pi is 180o
5(180o) 12900o
12o
=75o
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