How To Find The Range Of A Function

Hi friends, in this blog we will see How To Find The Range Of A Function. Function is taken to show a association between set of inputs values and set of outputs values in such a way that every value of input is associated to exactly one value of output. Let we have a function f (r) = r / 6 (f of ‘r’ is ‘r’ divided by the value 6") is a function. So if we are going to put the value of ‘r’ as 6 then we get the value of function as 1, it can be written as: f (6) = 6 / 6 = 1,

Now we will understand how to calculate range of a function. In function, all the ‘y’ coordinate values are said to be range of a function. In the same way we can also find out the domain of a function, all the possible terms of ‘x’ coordinate are known to be domain of a function. Let we have given some values (12, -18), (-71, 84), (53, -42), (-25, 17), then range of function is all the ‘y’ coordinate terms.

Domain = 12, -71, 53, -25.

Range is all ‘y’ coordinate values,

Range = -18, 84, -42, 17.

Let's understand that how to calculate the range of a function. Some steps are taken to calculate the range of a given function which are shown below:

Step1: To calculate the range of a function first have to take a function which contains ‘x’ and ‘y’ coordinates.

Step2: As we discuss above the range of a function is all ‘y’ coordinates values.

Step3: In above function the terms of ‘x’ and ‘y’ coordinate are there then we can easily calculate the range and domain of a function.

In this way we can easily find out the range of a function.

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How to Find the Domain of a Function

Hi friends, we will study different types of functions such as linear function, quadratic function and so on. Here we will see How to Find the Domain of a Function. Function can be defined as a tool used to confirm the relationship between the given values. Now we will see how to find the domain of a function. Generally, functions are defined as f (u) here ‘u’ is the value that we given it. Like, f (s) = s / 2 ('f' of 'p' is divided by 2) is a function. Here we can find out different values on putting the different value of variable s.

For calculating the domain of function first we need to discuss about what the domain of a function is. If we select the entire values of x - coordinates in the given function, then these x- coordinates values are said to be the domain of a function. In same way we can also find the range of a function, all possible ‘y’ coordinate values are known as range of a function. Let we have some values (4, -6), (-3, 7), (15, -9), (-19, 8), then domain of function can be obtained as:

The domain of a given function = 4, -3, 15, -19.

Range is all ‘y’ coordinate values,

Range = -6, 7, -9, 8. Now we will understand that how to find domain of a function in details. We will see some steps to calculate domain of a function:

Step 1: To find the domain of a function first we assume a function which contains ‘x’ and ‘y’ coordinates.

Step 2: As we discuss above the domain of a function is all ‘x’ coordinates values.

So if we have values of ‘x’ and ‘y’ coordinates then we easily find the domain and range of a function. This is all about the domain of a function.

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graphing exponential functions

In the previous post we have discussed about How To Find The Range Of A Function and In today's session we are going to discuss about graphing exponential functions. Exponential functions are the kind of functions that can be represented in ex. Here the variable e can be defined as a number that has approx value equal to 2.7183. The basic reason behind the popularity of exponential functions is that it is a function that models a relationship between constant change and a proportional change of independent variables. The most basic exponential function’s notation is given below:

y = e^x

In the above given notation the value of y depends on the exponential value of x. In the same aspect, the value of get increases faster when the value of x increases. Here we are going to discussing how to Graphing Exponential Functions. In this concept we study how to plot a exponential functions on a graph. Before discussing about this topic we need to clear one thing that we required a little bit knowledge about a graph that helps us on plotting exponential function’s value on graph. The graph of exponential function’s always lies above the x – axis and some time get very closer to the x – axis at the negative side of x but in both cases it do not touch the x – axis. So, finally at the time of graphing exponential function we need to follow some steps that are given below: (know more about graphing exponential functions  , here)

I ) From starting a table that records all the values of y which is calculated on the basis of y.

II ) To calculate the value of y we required to use the properties of exponents .

III) When above given both step completed then plot the points on graph.

IV ) After that draw a line according to the plotted points.

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How To Find The Range Of A Function

Range is the difference between greatest data value and least data value.
Suppose there is two set of data value first  one is X( a,b,c,d) and second one is Y(p,q,r,s).
If a function ‘f’is defined from set X to set Y then for f:X->Y , set x is called the domain of function f and set y is called co-domain function of f. The set of f images of the elements of x is called the range of function .
So in this case
Range = p,q,r

How to find the range of a function
#The easiest way to the range is on the graph. The range of the function is the range of y values it enclose.
#If domain is given, the range is the range of y values  corresponding to x values in the domain.
# check if function repeats. Any function which repeats along the x-axis will have the same range for the entire function.
Example: sin(x) has a range of -1
#The domain of a function’s inverse function is equal to that function’s range.
#Take a derivative of the graph. Find the y values at these points and the ends of the domain and take the most extreme ones as the boundary of the range. (know more about Range, here)

 Example: find the range of the function : g(x)= x/3+5 if the domain is -6,-3,0,3,6
Solution: we know that domain is the values x takes. Range is the corresponding values of the function takes.
Here g(x)= x/3+5.
For example when x=-6,we get -6/3+5=3
When x=-3, we get -3/3+5=4
When x=0, we get 0+5=5
When x=3, we get 3/3+5=6
When x=6, we get 6/3+5=7
So the range is (3,4,5,6,7)
In cbse syllabus for class 9th 2013 , specific heat equation is given by
Q = mc delta T
Where Q is amount of heat needed
M is the mass
C is specific heat capacity
Delta t = temperature difference.

Cartesian Product

In the previous post we have discussed about Differential Calculus and In today's session we are going to discuss about Cartesian Product. An ordered pair, usually denoted by (x , y) is pair of elements x and y of some sets. Like the Cartesian product of two sets A and B is set of those pairs whose first co coordinate is an element of A and second co-ordinate is an element B. The set is denoted by A x B and is read as ‘A cross B’ or ‘product set of A and B’. Basically these sets are work as ordered pair usually denoted by (x, y) is a pair of element x and y of some sets, which is ordered in the sense that (x, y) ≠ (y, x) whenever x≠y. Here x is called first co-ordinate and y is called second co-ordinate of the ordered pair (x, y), for example ordered pair (1, 2) and (2, 1) consist of same element 1 and 2 but they are different because they represent different points in the co-ordinate plane. (know more about Cartesian Product, here)

Now we use this concept in Cartesian product as following manner:
A x B = (x, y): xϵ A  É… yϵ B, A and B are different sets which are multiplying with each other.
Let the value of set  A = 1, 2, 3 and the value set  B=3, 5;
A x B=1, 2, 3 x 3, 5;
=(1, 3), (1, 5), (2, 3), (2, 5), (3, 3), (3, 5) (Here we get many ordered pair of A x B  which are called Cartesian product value of A x B),
And B x A=(3, 1), (3, 2), (3, 3), (5, 1), (5, 2), (5, 3) (Here we get many ordered pair of B x A which are called Cartesian product value of B x A ),
A x B ≠ B x A (it means both product are not same).
Similarly, we can define Cartesian product for n sets A1, A2, A3 …….An
A1, A2, A3 …….An  = ( x1, x2, x3 …….xn  )  x1 Ïµ A1 É…  x2ϵ A2 É…  x3ϵ A3 ……………. É… xnϵ An
The element (x1, x2, x3 …….xn  ) is called as n-type elements.
In this way we can solve the all Cartesian product problem.
Now we discuss what is Logarithmic Differentiation? We know exponent expression is defined as in the power expression like if y = ax, where x is logarithmic of y to the base a, in this case we will use the logarithmic differentiation. ISEET Physics syllabus helps students for their better study.

Differential Calculus

In the previous post we have discussed about limit laws and In today's session we are going to discuss about Differential Calculus. Dear students in today’s class we will study a very important and very interesting topic that is calculus. It is a branch of mathematics. We will take a brief idea about this topic.“Calculus” is a Latin word which means a tiny stone that is used for counting. It is a branch of mathematics which is basically based on functions, limit, differentiation and  integration. It constitutes of two major branches. One of which is differential calculus and another is integral calculus. Differential calculus is the study of change of limit, function and derivative . Differential calculus has vast  applications in the field of science, engineering and  sometime in economics also.  (know more about Differential Calculus, here)
It is also called that differential calculus is a very important method or system of calculation which is explained by the representative manipulation of expressions. There are many examples of differential calculus. Differential Calculus was the first success of modern mathematics and it is very tough to avoid its importance.  It only clears more efficiently the system of mathematical analysis.
Calculus is generally developed by manipulating very small quantities. Calculus has been used in every branch of the computer science, physical science, statistic, engineering, economics, business,etc. Calculus can also be used in combination with other mathematical branches.
Lets take a example: it can be used in theory of probability to settle on the probability of a nonstop arbitrary variable from an assumed density function. it can also be used with linear algebra to determine  the "best fit" linear approximation.
Calculus is also applied to evaluate estimated solutions to equations.  It is the very important way to solve differential equations in most applications.
So, we can say that calculus has very wide applications in the field of mathematics and even imagine of mathematics is not possible without “Calculus”.
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limit laws

Limit is used to define the value in which the function is approaches as an input. Limit is also used in calculus and also used to define the continuity function. Let’s talk about the limit laws. In mathematics, there are different types of laws which are given below. Now see all the limit laws one by one.
1.      Addition law: - The additive law is given by: Let the lim _{y ⇥b} f (y) and lim _{y ⇥b} g (y) both are exist then
lim _{y ⇥b} f (y) + lim g (y) = lim _{y ⇥b} f (y) + lim _{y ⇥b} g (y).
2.      Subtraction law: - The subtraction law of limit is given by: Let the lim _{y ⇥b} f (y) and
lim _{y ⇥b} g (y) both are exist then
lim _{y ⇥b} f (y) - lim g (y) = lim _{y ⇥b} f (y) - lim _{y ⇥b} g (y).
3.    Constant law: - The constant law of limit is given as: Let ‘c’ is a constant, and the limit lim _{y ⇥b} f (y) exist, the constant law can be written as: lim _{y ⇥b} c. f (y) = c. lim _{y ⇥b} f (y).
4.      Multiplication law: - The multiplication law is given by: Let the lim _{y ⇥b} f (y) and
lim _{y ⇥b} g (y) both are exist then
lim _{y ⇥b} f (y) . lim g (y) = lim _{y ⇥b} f (y) . lim _{y ⇥b} g (y). (know more about limit laws, here)
5.      Division laws: - The division law of limit is given by: Let the lim _{y ⇥b} f (y) and
lim _{y ⇥b} g (y) both are exist and lim _{y ⇥b} g (y) ≠ 0, then the division law can be written as: lim _{y ⇥b} f (y) / g (y) = lim _{y ⇥b} f (y) / lim _{y ⇥b} g (y). This is all about the limit laws. Now we will see the Triangle Inequality Theorem. It says that the sum of two sides of a triangle is always larger than the third side. To get more information then prefer online tutorial of cbse syllabus for class 9 and In the next session we will discuss about Differential Calculus.