Presentation of Mathematics

On the topic

Non Linear Functions, Their Graphs, and Application

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).

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

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y

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.

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𝟑 𝒙+𝟒 𝒚=𝟏𝟎Types of Polynomial

Function

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

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y

𝟑 𝒙𝟐+𝟒 𝒙=𝟏𝟎Types of Polynomial

Function

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

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y𝒚=𝒙𝟑

Types of Polynomial

Function

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

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30 y

𝐲=(𝒙 −𝟑 )𝟑

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

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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

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)

Sketching the graph of

Demand and Supply

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Equilibrium

P p

Quantity

Pri

ce

Supply Curve

Demand Curve(50,116)

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.

Examples:

solution, Step 1: Step 2: Step 3:

Step 4: If

-3 -2 -1 0 1 2 3 40

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𝑦=4𝑥+2

Examples:

2. Solution,

Step 1: Step 2: Step 3:

Step 4: If

𝑦=4−𝑥+2

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Any Queries!!!

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