What Is A Set Of Ordered Pairs Called

Introduction to function

The function in the mathematics refers to an expression or the rule which helps in defining relationship in between one variable and that of another variable. The functions are found to be ubiquitous in the field of mathematics and they are of great importance for the formulation of physical relationships within the sciences.

Function Notation

The function takes the input and it is instrumental in producing the output. Within function notation, f (x), f is indicative of name of the function, x refers to input variable and f (x) can be labelled as the output.

The function notation formula can be stated to be f(x) = x ². There exist some examples which helps in understanding application of that of function notation formula.

Example 1

Y can be said to be the function of x and function definition can be stated to be:

y- f (x) = 1/ 1+ x²

Find output values of function for that of x= 0, x= -1 and that of x= Square root of 2 by making use of the function notation formula.

Solution:

The given function notation formula can be stated to be:

Y= f (x) = 1/ 1+ x²

We can substitute the values of x and it can help us to arrive at the right answer

Thus, f (0) = 1, f (-1) = ½ and f (square root of 2)= 1/3

Example 2

A cone is found to have the variable height h and it has the variable base radius r, however sum of h and the r is found to be fixed. The cone is found to be made of the material of the density p. Express mass m of the cone which acts as function of the height h.

Solution:

Volume V of the cone is found to be given by:

V= 1/3 π r² h

Let fixed sum of h and r be that of k. Hence, r= k-h and hence:

V= 1/3 π h (k-h) ²

By making use of the function notation formula, mass of cone can be expressed as function of the h; m can be found to be p times that of volume V:

M= f(h)= pV = 1/3 π ph (k-h) ²

The answer: Thus m= f (h) =p V= 1/3 π ph (k- h) ² which can be stated to be required cell function.

Types of functions

1. Linear function

The linear function is indicative of the function which has one or the two variables and it does not have any exponents.

1. Quadratic function

The quadratic functions is indicative of the form f(x)= ax ² + bx+ c in which a, b and c refer to the numbers which are not equal to that of zero.

1. Cubic Function

Within mathematics, the cubic function is indicative of function of form f (x) = ax ³ + bx²+ cx + d in which the co-efficients a, b, c and d are found to be the complex numbers and variable x is found to take the real values and that of a≠ 0. It can be stated to be both polynomial function of the degree 3 and that of the real function. The domain and that of co-domain are found to be set of real numbers.

1. Logarithmic function

It can be stated that within mathematics, logarithmic function can be stated to be inverse function to that of exponentiation. The logarithmic function can be defined as

For x> 0, a> 0, and a ≠ a^y

The function can be given by:

f (x)= log _a x

The base of algorithm can be stated to be a. It can be said to be related to log base a of that of x. The 2 common bases which can be found within the logarithmic functions can be stated to be of the base 10 and that of base e.

Exponential function

The exponential function is indicative of mathematical function in form of f(x) =a ^x, in which “x” is the variable and “a” is found to be the constant that is called base of function and it has to be greater than that of 0. The exponential function which is found to be commonly used are the transcendental number e and that is found to be approximately equal to that of 2.71.

Trigonometric function

The trigonometric functions are indicative of the real functions that is related to angle of the right-angled triangle to the ratios of the two side lengths. They can be found to be widely used within the social sciences which are found to be related to the geometry, solid mechanics and navigation. They are found to be simplest periodic functions and they can be used for the studying of periodic phenomena with the aid of Fourier analysis. The trigonometric functions are be widely used within the field of modern mathematics which are sine, cosine and tangent.

Evaluation of functions

The evaluation of function means that finding value of the f (x) = … or y… which corresponds to that of given value of the x. For doing this, there has to be replacement of all x variables with x that has been assigned. For example, in the event of individuals being asked for evaluating f(4), then x has to be assigned value of that of 4.

Steps for evaluating functions

There are various steps which can be used that can aid in the evaluation of functions. The output kind has to be determined on the basis of input record type. The storage has to be allocated in regard to the result in the event of it being necessary. The Function Evaluator has to be acquired which has to be bound to input record and that of result storage. There has to be invoking of evaluator on that of Function Evaluator. It has to be repeated as necessary and it has to be carried out.

F(x) = 3x + 6, find f (2)

It means that function has to be evaluated in the event of x being assigned value of that of 2. First step can be instrumental in replacing all the x with that of 2. The function can be evaluated by the aid of following order of the operations (BEDMAS).

f (x)= 3x + 6

It can be stated that we have:

F (2)= 3(2) + 6

= 6+ 6

=12

Advantages of function notation

The advantages of making use of function notation is that it can aid in the identification of independent variables with a great deal of ease. It can be useful for identifying element of the function that has to be examined.