Chap 2 Section2

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

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Section 2.2 The Graph of a Function 109 Version: Fall 2007 2.2 Exercises Perform each of the following tasks for the functions defined by the equations in Exercises 1 - 8 . i. Set up a table of points that satisfy the given equation. Please place this table of points next to your graph on your graph paper. ii. Set up a coordinate system on a sheet of graph paper. Label and scale each axis, then plot each of the points from your table on your coordinate system. iii. If you are confident that you “see” the shape of the graph, make a “leap of faith” and plot all pairs that sat- isfy the given equation by drawing a smooth curve (free-hand) on your coordinate system that contains all previously plotted points (use a ruler only if the graph of the equation is a line). If you are not confident that you “see” the shape of the graph, then add more points to your table, plot them on your coordinate system, and see if this helps. Continue this process until you “see” the shape of the graph and can fill in the rest of the points that satisfy the equation by drawing a smooth curve (or line) on your co- ordinate system. 1. f ( x ) = 2 x + 1 2. f ( x ) = 1 x 3. f ( x ) = 3 1 2 x 4. f ( x ) = 1 + 1 2 x 5. f ( x ) = x 2 2 6. f ( x ) = 4 x 2 Copyrighted material. See: 1 7. f ( x ) = 1 2 x 2 6 8. f ( x ) = 8 1 2 x 2 Perform each of the following tasks for the functions Exercises 9 - 10 . i. Set up a coordinate system on a sheet of graph paper. Label and scale each axis. ii. Use the table feature of your graph- ing calculator to evaluate the func- tion at the given values of x . Record these results in a table next to your coordinate system on your graph pa- per. iii. Plot the points in the table on your coordinate system then use them to draw the graph of the given function. Label the graph with its equation. 9. f ( x ) = x 4 at x = 4 , 5, 6, 7, 8, 9, and 10.
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