Basic Math Concepts In Calculus And Precalculus

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One of the subjects I tutor often is precalculus. Students have many problems with precalculus. These problems range from exponential functions to logarithmic functions. Especially confusing to many people are trigonometry functions. Other topics that they have difficulty with in this subject include the definition of a function along with asymptotes, algebraic groups, the unit circle and the concepts of domain and range.

Precalculus centers around the concept of the function. Simply put, a function is a mapping of one set of numbers onto another set of numbers. However, the set of numbers that are being mapped to get only mapped from one unique number and not from many. Otherwise, it is not a function. The set of numbers that are being mapped from is called the domain while the set of numbers being mapped to by the function is called the range.

Once the concept of the function is understood then many different types of functions are explored. The following types of functions are studied in precalculus: polynomial functions, rational functions, exponential, logarithmic, trigonometric and others. Understanding how these functions work is important if a student will continue onto calculus. Normally, polynomial functions are learned during algebra. The rational functions which are learned during algebra or precalculus represent a
fraction with a polynomial in the numerator and one in the denominator.

At some point, the concept of inverse functions is introduced. Students have always confused inverse functions with reciprocal functions. The two are usually not the same. The inverse function undoes the operation of its related function. If a function that has a certain input, such as x for instance, was input into the inverse function, the inverse function would undo the original function and return the input x. One of the ways to solve for the inverse function is to substitute the variable y for f(x), swap the x with the y and solve for y. The result is the inverse function. Linear, exponential, logarithmic and trigonometric functions all have inverse functions which will allow them to be solved for x. When taking precalculus, a student is expected to learn how to use an inverse function to isolate a particular
variable.

Later on when the student starts learning trigonometry they start learning about sine & cosine functions as well as tangent, cotangent, secant and cosecant functions. First of all these functions relate the the sides of a triangle to a particular angle. The trig functions produce a ratio of two sides of a triangle that falls on the unit circle. When given a particular angle, the student is expected to find the ratio of any two sides. The trig functions are especially important because they are used throughout calculus and higher math and are used everywhere in the real world including science, engineering and business. It is important for the student to master precalculus in order to do well in succeeding courses.

Tutoring can help students who are having trouble with basic math concepts such as the function. Given enough time, students can figure out most of precalculus on their own. Sometimes, however, they get behind and have trouble catching up. A good math tutor, however, can get them up to speed.

I am a science and math tutor who provides tutoring in the Boston area. I provide one-on-one private tutoring for elementary grade levels as well as for high school and college. I tutor a wide range of subjects. For example, in math, I tutor algebra, geometry, precalculus, calculus and statistics as well as basic math. In the sciences, I provide tutoring in physics, chemistry and biology. In computer science, I tutor C, C++, java and other programming languages. Other fields of knowledge include economics, business, English and college writing.

I mostly tutor in Boston, Massachusetts and the towns surrounding the Boston North Shore. As a Boston Math Tutor I’ve helped many students overcome their math difficulties.

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