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# worksheet_piecewise - MATHEMATICS 111 PIECEWISE-DEFINED...

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MATHEMATICS 111 - PIECEWISE-DEFINED FUNCTIONS Problem #1. Let f ( x ) = 3 x - 1 if - 5 x < 1 4 if 1 x 3 6 - x if 3 < x 5 . (a) Evaluate f at x = - 3 , 1 , 2 , 5 . (b) On what interval is f constant? (c) Sketch a graph of f . Is f continuous on its domain? (d) Find the x-value(s) where f ( x ) = 2 . Problem #2. Let g ( x ) = - 2 x - 6 if - 8 x ≤ - 2 x if - 2 < x < 2 1 2 x + 1 if 2 x 8 . (a) Evaluate g at x = - 8 , - 2 , 2 , and 8 . (b) For what x-values does g ( x ) have a positive slope? (c) Sketch a graph of g . Is g continuous on its domain? (d) Find the x-value(s) where g ( x ) = 0 . Problem #3. Let h ( x ) = - 2 if x < - 2 0 if - 2 x < 0 3 x if 0 x 4 . (a) Determine the domain of f . (b) Evaluate f ( - 2) , f (0) , and f (3) . (c) Graph f . (d) Is f continuous on its domain? Problem #4. Let f ( x ) = 3 if - 4 x ≤ - 1 x - 2 if - 1 < x 2 1 2 x if 2 < x . (a) Determine the domain of f . (b) Evaluate f ( - 2) , f (0) , and f (3) . (c) Graph f . (d) Is f continuous on its domain? 1

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2 PIECEWISE-DEFINED FUNCTIONS - MATHEMATICS 111 Problem #5.
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worksheet_piecewise - MATHEMATICS 111 PIECEWISE-DEFINED...

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