Step Functions and Piecewise FunctionsA series of free Intermediate Algebra Video Lessons from Brightstorm online Algebra series.
Step Functions Some functions are not easily written as a formula. On a graph, a step function looks like a flight of stairs. The graphs of step functions have lines with an open circle on one end and a closed circle on the other to indicate inclusion, like number line inequality graphs. A rounding step function tells us to round a decimal number to the next whole integer or the previous whole integer.
Piecewise Functions In real world situations it can be difficult to describe events with a single smooth function. We sometimes need to use piecewise functions to describe these situations. Piecewise functions are functions that are defined to be smooth functions for specific intervals of the independent variable, most commonly the x-variable.
Using a Graphing Calculator One tool used throughout Algebra, Trigonometry, and Calculus is a graphing calculator. One thing using a graphing calculator is helpful for is solving systems of equations. We can solve systems of linear equations by using a graphing calculator and matrices. We can also solve systems of nonlinear equations by using a graphing calculator to graph their equations and find the intersection.
Common Algebra Mistakes Some of the most common algebra mistakes come from misunderstanding the order of operations or what is commonly known as PEMDAS. We must keep in mind that the multiplication and division are done at the same time in the order of operations, as are addition and subtraction. The most important way to help not make these common algebra mistakes is by practicing and being aware of pitfalls.
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