Thursday, May 16, 2013

Graph Logarithmic Functions


A logarithmic function relates the output corresponding to the logarithms of the variables. In many applications in real life, it is easier to study the output to the logarithmic values of the variable rather than the values of the variables. This is because; in certain cases the output increases very rapidly with even nominal increases of values of the variables.

Since the logarithm picks up only the increase in the exponent size, the increase rate is controlled to smaller figures. For example if a function is described as f(x) = x, for every1 increase of the variable, the function rises by 1. On the other hand if we define a function g(x) = log [(f(x)] = log (x), then the function rises by 1 only for every 1 increase of exponent of 10.(Here as per normal conventions we referred ‘log’ to mean logarithm to base 10).

In other words, a logarithmic-function has a low increase for large inputs. But however much we explain, the concept can be more clearly understood with a logarithmic function graph. Always a visual presentation is much more effective than verbal algebraic explanation. Thus graphing logarithmic functions have taken a very important place in algebra especially in the study of functions.
Because of the large variations of scales of the input and output in such functions and also because of the domain restrictions one must adopt the correct technique to graph logarithmic functions.

The following may be used as some tips to do the graphing for functions of logarithm.
1) First find the domain of the given functions. Remember that logarithms are defined only for positive expressions. So accordingly determine the domain and start graphing only from the minimum domain value. This will give an idea about the scaling the variable axis.
2) According to the domain of the function, determine the range. You can determine a practical range so that graph is properly sized. This will help in selecting proper scale for the output or function axis.
3) Next find the x-intercept and y-intercept. In some cases one or even both may not exist at least in the selected domain and range of the graph. Plot these points on the set of coordinate axes.
4) Make a table of values for a few points (practically it will be only 2 or 3) selecting compatible values of the variables. For example, if f(x) = log (x), make the table for values of powers of 10. Plot the table values on the same set of axes.
5) Draw a smooth curve connecting all points that are plotted. The ends of the curve should have arrow heads in the appropriate directions to indicate that the function is continuous.

Tuesday, April 30, 2013

Quadratic functions


Let us first see how quadratic functions are defined. A function is a relation between two or more variables which is one to one and onto. If the independent variable is single with degree 2 and the dependent variable is of degree 1, then the function is said to be quadratic. That is, the output of the function is related to the square of the input.

The general form of a quadratic function is y = f(x) = ax2 + bx + c, where a, b and c are all constants. Obviously, the constant a cannot be 0, in which case the degree of the variable will be no longer 2 and hence the function will not qualify as quadratic function.

Quadratic-functions are the most prominent functions in algebra as many practical situations can be cited as quadratic functions examples. Thus the knowledge of solving quadratic functions is extremely important. The solving can mean in two types of solving. One is to find y for a given value of x. But this is very simple task to do and has no great practical implications.

On the other hand, for a given value of y, to solve forx is extremely important. This is what generally referred as solving quadratic functions. The very first exercise is to solve for solve for x,when y = 0. The values of x under such conditions are called as the zeroes of the function or the x-intercepts of the function. In case of linear functions y-intercepts are more prominent but in case of functions of quadratic form, the x-intercepts are more prominent.

In certain cases, you may find the solutions to be imaginary and at a later stage we will explain the implication of such cases.

A quadratic function can be transformed to a quadratic equation for a given value of y. That is, the constant term is adjusted accordingly and is equated to 0. There are many methods of solving for the variable. The easiest method, if possible, is to factor the trinomial as the product to two binomials and apply the zero product property. In cases where factorization is not possible, one can use the quadratic formula and find the solutions.

We cannot predict for sure, the shape of a graph for a given function except in two cases. In case of a linear function, the graph is a straight line. The shapes of graphs of quadratic functions are invariably vertical parabolas. The points of intersections of the parabolas with x-axis are the zeroes of the function. If there are no such intercepts, the zeroes of the functions are imaginary.

Wednesday, April 3, 2013

The Art of Simplifying Rational Expressions


The concept of simplifying rational expressions can be understood only after the studying the basics. Once the basics are clear, it becomes very easy to solve these. The concept of solving algebraic equations can also be learnt from these basics.

Once this is understood simplifying algebraic expressions can be very simple. Basic algebraic expressions will contain the arithmetic operations of addition, subtraction, multiplication and division. They also contain constants and variables. The value of constants does not change throughout and the value of the variables can change. This is the basic difference between the two.

To simplify rational expressions one must understand what the definition of these expressions is. These can be written with the fractions. The denominator in the fraction must not be zero; otherwise it is difficult to define the fraction.

The degree of the expression plays a very important role in deciding the method to solve the expression. The question how to simplify rational expressions can be understood only if the basics are understood. It is important to learn the concept of polynomials to understand this concept. Ratio of the polynomials can be treated as an expression representing the concept. The concept of ratio is very clear and simple to understand.

There can be various terms in the polynomial. These terms can be rational or need not be rational in nature. But this will be true only for the real numbers. The complex numbers do not come into the picture here. The complex numbers consist of a real part and an imaginary part in them.

So, this cannot become a part of the polynomials that appear in the ratio. The polynomial that appears in the denominator must not be reducible to zero otherwise the whole expression is valid.This concept is also useful in geometry. The expression can be represented graphically. Simplifying these fractions can be learnt from the simplification of simpler fractions. The process in simplification is very simple.

The common terms that are present in both the numerator and the denominator are cancelled, so that the common terms do not appear twice. This is the basic idea of simplification. The same process is followed in simplifying these expressions as well. The polynomials must be reduced into simpler terms. If there are any common terms in the numerator and the denominator they must be cancelled. This makes the term simpler and easy to understand.

Wednesday, March 27, 2013

Mixture Problems as Words


We are solving the equations in mathematics always having direct problems but when we are solving the problems in the word or description format then it is known to be as mixture problems. Formation of the question or getting the problems in the form of word problems is the approach to check your analytical skills.

It is very useful in the future profits as if you go further in the studies then you have to face the Operational Research type of subject or the optimization techniques used in the process of various functional aspect of the organization.

When the problem comes in the word format then you have a better experience to do that it means that you have to do the lot of problems before attempt the problems given in your papers. As it is must to know the formats in the word problems. Algebra mixture problems are creating a mix of two or more than two things to determine something related to quantity of the mixture problems.

It is the conversion of qualitative analysis into quantitative analysis. Say for example of mixture problems in algebra like if the trains are moving in a same direction and both the speeds of the train is 7km/s then tell us the relative speed of both the trains?

This is an example of the problems which is word problem. Solving this kind of the equation you have to focus on what the question want and then proceed further to reach to the final equation.

The other part of solving the equation is form the tabular form as when the polynomial type of the equation is given and then solves it as per the logical reasoning. Mixture problems in algebra is to mix up the qualitative type of problems in a quantify manner to check the data interpretation of yours while solving this kind of problems.

As if you understand these kinds of problems then you are able to solve all the problems in the mathematics. Operation research is a big scope for good data interpreter and it works in your competitive advantage also. So try to better solve more and more number of problems based on word problems to increase your IQ level.

Few tips we want to share is use go through the problem and in rough do the analysis part what is given in the problem and then to start the solution. Procedure wise solve the question to reach the final goal what you want to achieve and make it as a sequential wise approach.

Wednesday, March 20, 2013

Concept of Simplification of Radicals


Various concepts are used in mathematics. Radicals are also one among them. They can also be represented with the help of a symbol. Basically they are used to represent the root of a number. The number can from the various number systems in mathematics. There are various number systems in mathematics.

The natural number system, whole number system, integer number system and real number system are some of them. There can also be irrational numbers and also complex numbers. The complex numbers have a real part and an imaginary part attached to them.

Do they are said to be complex numbers. The operations that are performed on real numbers like addition and subtraction can also be performed on the complex numbers as well. But to perform these operations one must be clear with the concept of the complex numbers.

The next question that arises is how do you simplify radicals in mathematics. The radicals have to be simplified in order to arrive at the final answer. The process to simplify radicals is quite simple. The root that has been applied to a number can be a square root, cube root and so on.

Sometimes fourth root can also be used. The number inside the square root symbol must be present two times then it can be taken out of the square root symbol. In case of cube root symbol it should be three times and in the case of the fourth root it should four times and so on.

In simplifying radicals practice is required; otherwise it becomes very tough to solve the problems. In mathematics practice is very important otherwise it will be very difficult to arrive at the final answer. Many mistakes can also be committed en-route to the answer. This can be avoided by proper practice.

There can questions to simplify radicals with variables like the simplification of normal radicals. The process is quite similar to the process of simplification of the radicals of the normal nature. Only proper practice can help one to reach at the right answer. There can be signs that can be used before the radical symbol.

The signs can be positive or negative in nature. Depending on the sign preceding the radical symbol the answer also changes. The positive denotes a positive number and a negative sign denotes a negative number. The magnitude also plays a very important role.

Thursday, March 7, 2013

Learn Math in a Smart Way by Expert Tutors


Get online tutoring and solve tough Mathematical problems in an easy way. Enhance your problem solving skills by taking required learning sessions with expert tutors. Experience the benefits of online learning service and improve your score in exams.

Expert guidance helps students in solving Math problems
                                                                                                                         
Math is an interesting subject but on the other hand, it seems quite tough to some people who don’t understand its concepts and formulas step-by-step. The subject mainly needs repetitive practice and concentration. Most importantly, Math is that kind of subject where students need assistance to brush up their knowledge and skills. Research suggests that an in-depth knowledge is the key requirement to solve any tricky Math problems. In that respect, students need a vast knowledge and they can easily get this required knowledge by taking assistance from expert online tutors. They can choose online Math tutors or live tutors as per their preference.

Math Problems and its instant solutions
Most of the students face difficulties while solving Math problems and they start searching the right solutions for these. In that matter, students can take assistance from online tutors who are available round the clock. With this service, they don’t need to travel to attend any learning session anywhere. They can schedule the required numbers of learning sessions at their preferred time from home. Moreover, they can opt for repeated sessions on a same topic and thus, they can achieve a good command over any topic. Additionally, the free worksheets make students familiar with the question pattern.

Online tutors guide students in solving Math homework and assignments

Have you faced difficulties in solving Math problems? Do you want to solve your Math problems in an easier way?  Then you can surely choose the online learning platform as it gives you a better understanding on any topic in a short span of time.  The online tutors are well trained and they can make you understand any concepts in a step-by-step manner.  Online tutor also helps you in completing your homework and assignments. Additionally, online service is quite safe and convenient and its user friendly features satisfy the students most.

Allied tools make online tutoring more effective
The advancement of new technologies has made online learning service more effective. Virtual white board and the attached chat box are some interactive tools that handle students-tutors communication in a better way. With these facilities, students can easily share their problems and documents with tutors and simultaneously, they can get the solutions instantly. Online assistance gives students a secure web environment and the attached chat box allows students to write their problems unhesitatingly. Hence, students can experience a better learning sessions and perform well in exam.

Friday, March 1, 2013

Plan your study schedule with your private tutor

Learning a topic in a step-by-step manner from a private tutor is quite advantageous and affordable. Choose a subject, schedule a session and get your doubts clear from an online experienced tutor who is available round the clock to guide you.

Why students needs Private Tutors

Class-room learning plays an imperative role in improving academic skills of students. However, some students hesitate asking their doubts to a tutor in a class-room environment. Learning new topics in class room is mandatory for every student but those who need extra help and more time to understand a subject must opt for online tutoring. Online help provides amazing opportunities to upgrade students overall skills and knowledge. A student gets personalized tutoring sessions with a preferred tutor from the comfort of home. Having a private tutor is a great help for those students who don't pay much attention in a class-room learning session. As they can easily get their doubts clear in a personal tutoring session and in flexible manner.

Role of Private tutors

Most of students search for personal learning assistance for completing the entire curriculum and assignments. It can possible through a private tutoring where a personal tutor will clear your doubts and help you to do better in exam and score good marks. Generally, students complete their homework and assignments with the help of books or other course materials. But getting help from a personal tutor is quite beneficial. Students get step-by-step solution to their queries in a flexible schedule as well as in secure environment. Hiring a live private tutor is quite expensive whereas online private tutors  
are inexpensive and flexible as they are available 24 hours to guide you.

Positive Aspects of having a Private Tutor

A private tutor not only covers all the topic of your curriculum but also improves you learning skills up to a great extent. With a private tutor, students get time flexibility and also get to learn various learning techniques that can be further used during examination time. It is observed that many students are more comfortable with private tutors as they can schedule a learning session on any subject at a preferred location. Apart from curriculum help, personal tutors also assist you while doing homework and assignments and also give you a last minute tip before an exam. The primary advantage of having a private tutor is that a student can cover up the topic, which he or she might have missed in the class-room session. Learning with a private tutor or an online tutor also makes you confident while dealing with difficult questions. An online tutor explains each topic in a step-by-step manner and at your pace so as to help you to attain maximum potential