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Chapter 3 Section 4: Library of Functions

Chapter 3 Section 4: Library of Functions. In this section, we will… Graph the Library of Functions (a.k.a. Basic Functions) Graph Piecewise Defined Functions. Constant Function. Linear Function. These graphs should: be straight (use a straight-edge) extend the length of the graph

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Chapter 3 Section 4: Library of Functions

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  1. Chapter 3 Section 4: Library of Functions • In this section, we will… • Graph the Library of Functions (a.k.a. Basic Functions) • Graph Piecewise Defined Functions

  2. Constant Function Linear Function • These graphs should: • be straight (use a straight-edge) • extend the length of the graph • have arrows on each end 3.4 Library of Functions

  3. Square Function Cube Function • These graphs should: • curve • extend the length of the graph • have arrows on each end • be symmetric 3.4 Library of Functions

  4. Square Root Function Cube Root Function • These graphs should: • curve • extend the length of the graph • have arrows • (the square root function will only have an arrow on one end) 3.4 Library of Functions

  5. Reciprocal Function • This graph should: • extend the length of the graph • have arrows on each end • be symmetric • hug the asymptotes Absolute Value Function • This graph should: • extend the length of the graph • have arrows on each end • be symmetric • be V-shaped 3.4 Library of Functions

  6. Example: Match each graph to its function. • reciprocal function • square function • constant function • cube root function • linear function • square root function • absolute value function • cube function 3.4 Graphing Piecewise Functions

  7. WISE FUNCTIONS • Graphing a Piecewise Defined Function • Note the domain of the function • Graph each piece and be sure to plot any endpoints of the piece • points included in the piece need a solid point • points not included in the piece will have an open circle A piecewise function is defined differently over different parts of its domain. 3.4 Graphing Piecewise Functions

  8. Example: Answer the following questions about the piecewise function: • Determine the domain of the function • Graph the function • Find • Find • Find • Use the graph to determine the range 3.4 Graphing Piecewise Functions

  9. Example: Answer the following questions about the piecewise function: • Determine the domain of the function • Graph the function • Find • Find • Find the intercepts 3.4 Graphing Piecewise Functions

  10. Example: Answer the following questions about the piecewise function: • Determine the domain of the function • Graph the function • Find • Find • Use the graph to determine the range 3.4 Graphing Piecewise Functions

  11. Example: Quahog Municipal charges residential customers $7.58 per month plus 8.275 cents per kilowatt-hour for the first 400 kilowatt-hours supplied within a month and 6.208 cents per kilowatt-hour for all usage over 400 kilowatt-hours in a month. • Write the monthly charge C for using x kilowatt-hour. • Graph the function • Find 3.4 Graphing Piecewise Functions

  12. Independent Practice You learn math by doing math. The best way to learn math is to practice, practice, practice. The assigned homework examples provide you with an opportunity to practice. Be sure to complete every assigned problem (or more if you need additional practice). Check your answers to the odd-numbered problems in the back of the text to see whether you have correctly solved each problem; rework all problems that are incorrect. Read pp. 242-248 Homework: pp. 248-251 #9-24 all, 29-37 odds, 47 3.4 Library of Functions

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