So, whether x is positive, negative, or zero. The expression |x| is read "the absolute value of x." Graph of the Piecewise Function y = -x + 3 on theinterval Ī special example of a piecewise function is the absolute valuefunction that states: These functions do not share the samepoint at x = 0, as the first contains that point (0, 3), whilethe second piece contains the point (0, 1). For example, the graphof y = -x + 3 on the interval and the graph y = 3x + 1on the interval. Some piecewise functions are continuous like the one depictedabove, whereas some are not continuous. However,at the point where they adjoin, when we substitute 1 in for x,we get y = 5 for both functions, so they share the point (1, 5). In the first piece, the slopeis 2 or 2/1, while in the second piece, the slope is 0. ![]() Notice that the slope of the function isnot constant throughout the graph. The graph depicted above is called piecewise because it consistsof two or more pieces. Graph of the piecewise function y = 2x + 3 on theinterval (-3, 1) ![]() ![]() Since the graphs do not includethe endpoints, the point where each graph starts and then stopsare open circles Note that theyspan the interval from (-3, 5). Consider the function y = 2x + 3 on the interval (-3, 1) andthe function y = 5 (a horizontal line) on the interval (1, 5).Let's graph those two functions on the same graph.
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