Posts Tagged ‘intervals’
Thursday, December 31st, 2009
How to Write Step Functions
Description
A detailed tutorial on how to write step functions. Step by step tutorial including several examples of how to write step functions for reference.
Overview
A step function, also called a staircase function, is a finite linear combination composed of several different intervals. They are considered to be a piecewise constant function. The graph of a step function is often expressed as steps, or a staircase, which is how it got its name. It simply looks like several disconnected lines, with alternate open and closed ends so that it easily passes the vertical line test for functions.
Tags: closed, combination, constant, diconnected, discrete math, ends, finite, function, graph, intervals, line, linear, lines, open, piecewise, staircase, step, test, vertical
Posted in Discrete Math | No Comments »
Tuesday, October 20th, 2009
How to Graph the Cotangent Function
Description
A detailed tutorial on solving the graph of the cotangent function. Step by step tutorial including several examples of how to solve the graph of the cotangent function for reference.
Overview
The graph of cotangent is very closely related to the graph of tangent and the graph of x cubed. The graph occurs in periods of pi, just like the tangent function. When graphing both the cotangent function and the tangent function together, they criss-cross to form an intricate looking curve. This is because tangent and cotangent are the opposite of each other - tangent is equal to one over cotangent.
Tags: amplitude, asymptote, cotangent, function, graph, intervals, period, pi, tangent, trigonometric, trigonometry, x, y
Posted in Trigonometry | No Comments »
Tuesday, October 20th, 2009
How to Graph the Cosecant Function
Description
A detailed tutorial on solving the graph of the cosecant function. Step by step tutorial including several examples of how to solve the graph of the cosecant function for reference.
Overview
The graph of cosecant is very closely related to the graph of secant. The graph appears to be many concave up and concave down curves placed in periods of 2pi. In reality, the local maximums and minimums on the graph of cosecant match up with the local maximums and minimums on the graph of sine, making it easy to line them up together. This is because sine and cosecant are the opposite of each other – sine is equal to one over cosecant.
Tags: amplitude, asymptote, cosecant, function, graph, intervals, maximum, minimum, period, pi, secant, sine, trigonometric, trigonometry, x, y
Posted in Trigonometry | No Comments »
Tuesday, October 20th, 2009
How to Graph the Secant Function
Description
A detailed tutorial on solving the graph of the secant function. Step by step tutorial including several examples of how to solve the graph of the secant function for reference.
Overview
The graph of secant is very closely related to the graph of cosecant. The graph appears to be many concave up and concave down curves placed in periods of 2pi. In reality, the local maximums and minimums on the graph of secant match up with the local maximums and minimums on the graph of cosine, making it easy to line them up together. This is because cosine and secant are the opposite of each other - cosine is equal to one over secant.
Tags: amplitude, asymptote, cosecant, cosine, function, graph, intervals, maximum, minimum, period, pi, secant, trigonometric, trigonometry, x, y
Posted in Trigonometry | No Comments »
Tuesday, October 20th, 2009
How to Graph the Tangent Function
Description
A detailed tutorial on solving the graph of the tangent function. Step by step tutorial including several examples of how to solve the graph of the tangent function for reference.
Overview
The graph of the tangent function looks a great deal like the graph of x cubed – just repeated several times. The graph of tangent is drawn in a period of pi – meaning a “line” is put down every pi spaces for a guideline on where to draw the graph – and hits all of the major points of the graph, also in intervals of pi. There is no amplitude of the tangent function because it extends up to both negative infinity and positive infinity in vertical directions.
Tags: amplitude, asymptote, function, graph, infinity, intervals, negative, period, pi, positive, tangent, trigonometric, trigonometry, vertical, x, y
Posted in Trigonometry | No Comments »
Tuesday, September 29th, 2009
Identifying Periodic Functions
Description
A detailed tutorial on how to identify a periodic function. Step by step tutorial including several examples of how to identify a periodic function for reference.
Overview
A periodic function is a function with repeating values. The values have to repeated in regular intervals, or periods. Well known examples of periodic functions are trigonometric functions, which constantly repeat over intervals of 2π. Periodic functions are often used to describe waves or other things that display periodicity, or the property of repeating over intervals.
Tags: Calculus, function, intervals, Math, periodic, periodicity, periods, repeat, repeating, trig functions, trigonometric functions, values, waves
Posted in Calculus | No Comments »
