This Crash Course covers solving step, periodic and piecewise functions graphically. Its interactive video, key takeaways section and summary exercise will provide a short review of the subject.
To understand how to solve step functions and piecewise functions graphically, you need to know what an interval represents and the different ways of writing one.
Also, understanding the rule and graphical representation of the linear function and the quadratic function will help you solve the piecewise function.
Step Functions
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For each step, there's an open (empty) point at one end and a closed (defined) point at the other. A closed point is part of the step in question, and an open point is not.
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In a table of values, a closed bracket represents a closed point, and an open bracket represents an empty point.
Periodic Functions
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The cycle of a function is the shortest interval of a repeating pattern on a graph.
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The period is the distance between 2 |x| values located at the two endpoints of a cycle.
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Two points located at a horizontal distance of one period have the same |y| value. For example, if the period is |12,| then |f(5) = f(5+12).|
Piecewise Functions
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Each piece of the function has its own rule.
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You must use the correct equation of the function to calculate the value of |x| or |f(x).|