Basics of Precalculus
Precalculus familiarizes students with the main concepts of calculus: functions, rates of change and accumulation. The study of change, calculus differs from geometry, the study of shapes, and algebra, the study of operations, while incorporating elements from both branches. More conceptual than other branches of mathematics, precalculus students need to understand the how and why of calculus to solve equations.
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Function
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A function is defined mathematically as a relationship between two variables when a rule assigns to each value of x a single value of y. Y is then a function of x. In the equation, y = 5x + 3, for every value of x, there exists one value for y. The possible values of x are termed the domain of the function. Once defined, the values of y that correspond to the values of x are called the range.
Rates Of Change
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The average rate of change is equal to the change in distance divided by change in time. An object's state does not change at a constant rate. For example, a object in free fall will gain momentum, but not at a constant rate. Using this formula can determine the average change in an object's velocity, growth or decay over a period of time. Precalculus students will also learn how to calculate the average rate of change of a function over an interval.
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Accumulation
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Provide the function of a changing quantity, and the integral will determine the amount of accumulation. The integral illustrates accumulation in the same manner that the derivative illustrates the rate of change; thus, the faster something changes, the faster it accumulates. A main focus of calculus, the concept of derivatives and integrals will be mentioned in precalculus so a basic understanding exists for future study.
Fundamental Theorem of Calculus
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The fundamental theorem of calculus defines the procedure of evaluating an antiderivative at both the upper and lower limits of integration and noting the difference. The properties of the theorem can calculate the interchanging limits of integration and linearity. Understanding the fundamental basics of calculus will enable students to grasp more complex theories as their studies advance.
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