Piecewise-defined functions -- Section 3.3 -- Graph the following: There is one function that has 2 different parts. Solve Step Check Part 1:  y =  f(x) = 3 when x < -2 Horizontal line y = -3 The open circle denotes that -2 is not  included since  x < -2 Click here for Lines Tutorial. f(-10) = -3   since -10 < -2 f(-6) = -3     since -6 < -2 f(-1.9) = -3  since -1.9 < -2 f(-2) = -2     since -2 > -2 Part 2:  y =  f(x) = x when x > -2 Linear function y = f(x) = x  The closed circle denotes that -2 is not  included since  x > - 2 Click here for Lines Tutorial. f(-2) = -2   since -2 > -2 f(0) = 0      since 0 > -2 f(2) = 2      since 2 > -2 f(4) = 4      since 4 > -2 Put both parts together... It is beautiful!  Graph the following:  [Solution]  Graph the following: There is one function that has 3 different parts. Solve Step Check Part 1:  y =  f(x) = -x - 2 when x < -2 Linear function y = f(x) = -x - 2  The open circle denotes that -2 is not included  since  x < -2 Click here for Lines Tutorial. f(-5) =  -(-5) - 2  = 3  since -5 < -2 f(-4) =  -(-4) - 2  = 2  since -4 < -2 f(-3) = -(-3) - 2  = 1since -1.9 < -2 Part 2:  y =  f(x) = 4 - x2 when  -2 <  x < 2 Quadratic function y = f(x) = x  The closed circle denotes that -2 and 2 is  included since  -2 <  x < 2 Click here for Quadratic Tutorial. f(-2) = 4 - (-2)2  = 4 - 4 = 0  since -2 <  -2 < 2f(-1) = 4 - (-1)2  = 4 - 1 = 3  since -2 <  -1 < 2 f(0) = 4 - (0)2  = 4 - 0 = 4  since -2 <  0 < 2 f(1) = 4 - (1)2  = 4 - 1 = 3  since -2 <  1 < 2f(2) = 4 - (2)2  = 4 - 4 = 0  since -2 <  2 < 2 Part 3:  y =  f(x) = x - 2 when   x > 2 Linear function y = f(x) = x - 2  The open circle denotes that 2 is not  included since  x > -2 Click here for Lines Tutorial. f(3) =  3 - 2  = 1  since 3 > 2f(4) =  4 - 2  = 2  since 4 > 2 f(5) = 5 - 2  = 3since 5 > 2 Put both parts together... It is beautiful! Notice the open circles and closed circles overlap.  Graph the following:  [Solution] Tutorials and Applets by
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