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Chapter 1: Linear Relations and Functions Section 1-7: Piecewise Functions Piecewise Functions z Different equations are used for different intervals of the domain. When graphing piecewise functions, the partial graphs over various intervals do not necessarily connect. z Remember a closed circle means the point is included and an open circle means the point is NOT included. Example #1 ⎫ ⎧ ⎪ ⎪2 if x ≤ -5 ⎪ ⎪ f ( x) = ⎨x + 4 if - 5 < x ≤ 4⎬ ⎪ ⎪ 1 ⎪ ⎪- x if x > 4 ⎭ ⎩ 2 z Graph z Here we have three intervals to look at on the x axis. When x is less than or equal to -5, y will always be 2 so this part of the graph is a horizontal line. When x is bigger than -5 but less than or equal to 4, we have a line with the equation x+4. And when x is bigger than -4 we have another line with the equation -1/2(x). The graph is a piecewise function. z It is a function because every part satisfies the vertical line test. Step Function z z A piecewise function where the graph looks like a set of stairs is called a step function. In a step function, there are breaks in the graph of the function. One type of step function is the greatest integer function. The symbol x means the greatest integer not greater than x. For example, 8.9 = 8 because 8 is the greatest integer not greater than 8.9. Example #2 z Graph f ( x) = 3 x Absolute Value Function z z The absolute value function is another piecewise function. The absolute value of a number is always nonnegative. Notice that the domain includes all real numbers, but the range includes only nonnegative real numbers. Graph f ( x) = − 2 x + 3 HW #6 z z z Section 1-7 Pp 49-51 #11,13,14,17,34,36