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By: Anne Kaufmann Kate Albertini Katie Fairman
What is a Piecewise Function? <ul><li>A piecewise function is an equation with multiple parts or pieces. It is made up of a series of different equations. </li></ul><ul><li>Each different equation covers a different set of input values (or numbers on the x-axis) over the domain. </li></ul><ul><li>A different piece of the domain is paired with each equation. The domain determines if the end points on the line are included or not. If the value is stated as equal to, then the value is represented with a closed circle on the line. If the value in the equation is stated as less than or greater than, but not equal too, then it is represented by an open circle. </li></ul>
x-1 if x<-1 F(x)= -1 if x=-1 x+1 if x>-1
Step Function <ul><li>A step function is a specific type of piecewise function in which the different pieces of the function resembles steps (or stairs) when graphed. </li></ul><ul><li>Two specific kinds of step functions are floor and ceiling functions. </li></ul><ul><li>A ceiling function makes the smallest integer less than or equal too x. The equation is shown on the next page (due to technical difficulties we could not write it on this page). </li></ul><ul><li>A floor function makes the largest integer greater than or equal to x. The equation is also shown on the next </li></ul><ul><li>page. </li></ul><ul><li>All rules for piecewise functions still apply. </li></ul>
Step Example: Floor function: Ceiling function: