Mathematics Graph of Non Linear functions
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Transcript of Mathematics Graph of Non Linear functions
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Presentation of Mathematics
On the topic
Non Linear Functions, Their Graphs, and Application
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What is Polynomial Function?
• A polynomial function is a function such as a quadratic, a cubic, a quartic, and so on
• The power of an indeterminate must not be negative.
A polynomial of degree n is a function of the form,f(x) = anxn+ an-1xn-1+an-2xn-2+……….+a2x2+ a1x + ax0
where the a’s are real numbers (sometimes called the coe cients ffi of the polynomial).
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Types of Polynomial
Function
Constant Function
The polynomial Function with power of variable zero is called Constant Function.
The graph of these functions is parallel to either axes.
, is an example of constant function.𝒚=𝒇 (𝒙 )=𝟐
-5 -4 -3 -2 -1 0 1 2 3 4 50
0.5
1
1.5
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2.5
y
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Linear Function
The polynomial Function with power of variable as Unity is called Linear Function.
The graph of these functions is straight lines.
, is an example of Linear function.
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
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Y
𝟑 𝒙+𝟒 𝒚=𝟏𝟎Types of Polynomial
Function
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Quadratic Function
The polynomial Function with power of variable two is called Quadratic Function.
The graph of these functions is parabola. , is an example of quadratic function.
-5 -4 -3 -2 -1 0 1 2 3 4 5
-20
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0
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y
𝟑 𝒙𝟐+𝟒 𝒙=𝟏𝟎Types of Polynomial
Function
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Cubic Function
The polynomial Function with power of variable three is called cubic Function.
The graph of cubic function either have no vertex or two vertex.
, is an example of Cubic function.
-4 -3 -2 -1 0 1 2 3 4 5 6
-30
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y𝒚=𝒙𝟑
Types of Polynomial
Function
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Horizontal Shifting
The graph of 𝑦= 𝑓 (𝑥−𝑎 ) , 𝑖𝑠 h𝑡 𝑒 h𝑔𝑟𝑎𝑝 𝑜𝑓 𝑦= 𝑓 (𝑥 )𝑚𝑜𝑣𝑒𝑑𝑎𝑢𝑛𝑖𝑡𝑠 h𝑟𝑖𝑔 𝑡 .
X
Y
Solution, Let And the graph of
For the graph of
-4 -3 -2 -1 0 1 2 3 4 5 6
-30
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0
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30 y
𝐲=(𝒙 −𝟑 )𝟑
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Vertical Shifting
The graph of 𝑦= 𝑓 (𝑥 )+𝒂 ,𝑖𝑠 h𝑡 𝑒 h𝑔𝑟𝑎𝑝 𝑜𝑓 𝑦= 𝑓 (𝑥 )𝑚𝑜𝑣𝑒𝑑𝑎𝑢𝑛𝑖𝑡𝑠𝒖𝒑 .
X
Y
Solution, Let And the graph of
For the graph of
𝐲=(𝒙 )𝟑+𝟏𝟎
-4 -3 -2 -1 0 1 2 3 4 5 6
-30
-20
-10
0
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20
30
y
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Hyperbolic Function
The function in the form of is called Hyperbolic Function.
The vertical asymptote is given by the equation
The horizontal asymptote is given by the equation
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Dealing with determination
of Equilibrium,
where demand function is a hyperbolic.
1. Solution:Step 1: The vertical asymptote is given by the equation Step 2: The horizontal asymptote is given by the equation Step 3: when
Step 4: The graph of So,
Or, Or, Taking Positive; Taking Negative; When Therefore, the curve passes through (499,1)
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Sketching the graph of
Demand and Supply
-100 0 100 200 300 400 500 600 700 800 9000
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Equilibrium
P p
Quantity
Pri
ce
Supply Curve
Demand Curve(50,116)
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Exponential and
Logarithm Functions
Any function is said to be exponential function if it is in the form:
Properties of Exponential Function:
If coefficient of
If coefficient of
The curve formed is asymptotic to positive x-axis.
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Examples:
solution, Step 1: Step 2: Step 3:
Step 4: If
-3 -2 -1 0 1 2 3 40
0.5
1
1.5
2
2.5
𝑦=4𝑥+2
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Examples:
2. Solution,
Step 1: Step 2: Step 3:
Step 4: If
𝑦=4−𝑥+2
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.50
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