General Mathematics- What is Function?, Study notes of Mathematics

This file contains lessons about what is functions and its examples

Typology: Study notes

2019/2020

Available from 02/11/2022

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Types of Functions:
1. Polynomial Function
-It is defined by the equation f(x) = anxn + an-1xn-1 + an-2xn-2+…+ a1x + a0, where n is a
non-negative integer and a0, a1, … an are real numbers.
-The symbol f(x) is read as “the function of x”
Kinds of Polynomial Function:
a. Linear function
odefined by f(x) =mx + b, a polynomial in the first degree whose graph is a line
b. Quadratic function
oA polynomial function defined by f(x) = ax2 + bx + c, also known as a
polynomial function in the second degree whose graph is a parabola
a) b)
Graph a represents a linear function, and graph b represents a quadratic function
2. Constant function
-Is a special polynomial function and defined by the equation bf(x) =c, where c .
In this function, each x value corresponds to one and only one y value. The graph of
which is a horizontal line
3. Rational Function:
- it is defined by the equation
f
(
x
)
=g(x)
h(x)
wherein g(x) and h(x) are both polynomial
functions. The function
f
(
x
)
=x+2
x2
is an example of a rational function
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Types of Functions:

  1. Polynomial Function - It is defined by the equation f(x) = a n

x

n

  • a n-

x

n-

  • a n-

x

n-

+…+ a 1

x + a 0

, where n is a

non-negative integer and a 0

, a 1

, … a n

are real numbers.

- The symbol f(x) is read as “the function of x”

Kinds of Polynomial Function:

a. Linear function

o defined by f(x) =mx + b, a polynomial in the first degree whose graph is a line

b. Quadratic function

o A polynomial function defined by f(x) = ax

2

  • bx + c, also known as a

polynomial function in the second degree whose graph is a parabola

a) b)

Graph a represents a linear function, and graph b represents a quadratic function

  1. Constant function - Is a special polynomial function and defined by the equation bf(x) =c, where c .

In this function, each x value corresponds to one and only one y value. The graph of

which is a horizontal line

  1. Rational Function:
    • it is defined by the equation

f ( x )=

g ( x )

h ( x )

wherein g(x) and h(x) are both polynomial

functions. The function

f ( x )=

x + 2

x − 2

is an example of a rational function

  1. Radical function - It is defined by the equation f ( x )=

n

g ( x ) wherein g(x) is a polynomial function and n

is a non-negative integer greater than 1. The equation f

x

2 x + 4 is an example of

a radical function

  1. Exponential Function
    • it is defined by the equation f

x

= a

x

, where a 0 ∧ a ≠ 1. The relation f(x) = 2

x

is an

example of exponential function

  1. Logarithmic function - It is an inverse of an exponential function and is defined bythe equation f ( x )=log

a

x ,

where a ≥ 0 and a ≠ 1. The function f ( x )=log

2

x is an example of a logarithmic

function

  1. Piecewise- Defined Function - A piecewise - defined function is a function whose definitions involve more than one

formula. An absolute value function is an example of a piecewise-defined function

- Consider the function f ( x )=| x |. This function can be defined using the definition of

absolute value