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**Unformatted text preview: **Section 4.1 Piecewise-Defined Functions 347 Version: Fall 2007 4.1 Exercises 1. Given the function defined by the rule f ( x ) = 3, evaluate f ( − 3), f (0) and f (4), then sketch the graph of f . 2. Given the function defined by the rule g ( x ) = 2, evaluate g ( − 2), g (0) and g (4), then draw the draw the graph of g . 3. Given the function defined by the rule h ( x ) = − 4, evaluate h ( − 2), h ( a ), and h (2 x +3), then draw the graph of h . 4. Given the function defined by the rule f ( x ) = − 2, evaluate f (0), f ( b ), and f (5 − 4 x ), then draw the graph of f . 5. The speed of an automobile travel- ing on the highway is a function of time and is described by the constant func- tion v ( t ) = 30, where t is measured in hours and v is measured in miles per hour. Draw the graph of v versus t . Be sure to label each axis with the appro- priate units. Shade the area under the graph of v over the time interval [0 , 5] hours. What is the area under the graph of v over this time interval and what does it represent? 6. The speed of a skateboarder as she travels down a slope is a function of time and is described by the constant function v ( t ) = 8, where t is measured in seconds and v is measured in feet per second. Draw the graph of v versus t . Be sure to label each axis with the appropriate units. Shade the area under the graph of v over the time interval [0 , 60] seconds. What is the area under the graph of v over this time interval and what does it represent? Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/ 1 7. An unlicensed plumber charges 15 dollars for each hour of labor. Let’s de- fine this rate as a function of time by r ( t ) = 15, where t is measured in hours and r is measured in dollars per hour. Draw the graph of r versus t . Be sure to label each axis with appropriate units. Shade the area under the graph of r over the time interval [0 , 4] hours. What is area under the graph of r over this time interval and what does it represent? 8. A carpenter charges a fixed rate for each hour of labor. Let’s describe this rate as a function of time by r ( t ) = 25, where t is measured in hours and r is measured in dollars per hour. Draw the graph of r versus t . Be sure to label each axis with appropriate units. Shade the area under the graph of r over the time interval [0 , 5] hours. What is the area un- der the graph of r over this time interval and what does it represent? 9. Given the function defined by the rule f ( x ) = , if x < 2 , if x ≥ 0, evaluate f ( − 2), f (0), and f (3), then draw the graph of f on a sheet of graph paper. State the domain and range of f . 10. Given the function defined by the rule f ( x ) = 2 , if x < , if x ≥ 0, evaluate f ( − 2), f (0), and f (3), then draw the graph of f on sheet of graph paper....

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