Chapter 4: Exercises with Solutions

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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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: 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 ) = 0 , if x < 0 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 < 0 0 , if x 0 , evaluate f ( - 2) , f (0) , and f (3) , then draw the graph of f on sheet of graph paper. State the domain and range of f .
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348 Chapter 4 Absolute Value Functions Version: Fall 2007 11. Given the function defined by the rule g ( x ) = - 3 , if x < - 2 , 1 , if - 2 x < 2 , 3 , if x 2 , evaluate g ( - 3) , g ( - 2) , and g (5) , then draw the graph of g on a sheet of graph paper. State the domain and range of g .
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