7. f(x) = 1 2 x f(x) = x f(x) = 4 x at x = 10, 8, 6, 4, 2, 0, 2, and 4.

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1 Section 2.2 The Graph of a Function Eercises Perform each of the following tasks for the functions defined b the equations in Eercises 1-8. i. Set up a table of points that satisf the given equation. Please place this table of points net to our graph on our graph paper. ii. Set up a coordinate sstem on a sheet of graph paper. Label and scale each ais, then plot each of the points from our table on our coordinate sstem. iii. If ou are confident that ou see the shape of the graph, make a leap of faith and plot all pairs that satisf the given equation b drawing a smooth curve (free-hand) on our coordinate sstem that contains all previousl plotted points (use a ruler onl if the graph of the equation is a line). If ou are not confident that ou see the shape of the graph, then add more points to our table, plot them on our coordinate sstem, and see if this helps. Continue this process until ou see the shape of the graph and can fill in the rest of the points that satisf the equation b drawing a smooth curve (or line) on our coordinate sstem. 1. f() = f() = 1 3. f() = f() = f() = f() = f() = f() = Perform each of the following tasks for the functions Eercises i. Set up a coordinate sstem on a sheet of graph paper. Label and scale each ais. ii. Use the table feature of our graphing calculator to evaluate the function at the given values of. Record these results in a table net to our coordinate sstem on our graph paper. iii. Plot the points in the table on our coordinate sstem then use them to draw the graph of the given function. Label the graph with its equation. 9. f() = 4 at = 4, 5, 6, 7, 8, 9, and f() = 4 at = 10, 8, 6, 4, 2, 0, 2, and 4. In Eercises 11-14, the graph of the given function is a parabola, a graph that has a U-shape. A parabola has onl one turning point. For each eercise, perform the following tasks. i. Load the equation into the Y= menu of our graphing calculator. Adjust the WINDOW parameters so that the turning point (actuall called the verte) is visible in the viewing window. ii. Make a reasonable cop of the image in the viewing window on our home- 1 Coprighted material. See:

2 110 Chapter 2 Functions work paper. Draw all lines with a ruler (including the aes), but draw curves freehand. Label and scale each ais with min, ma, min, and ma. Label the graph with its equation. 11. f() = f() = f() = f() = Each of the equations in Eercises are called cubic polnomials. Each equation has been carefull chosen so that its graph has eactl two turning points. For each eercise, perform each of the following tasks. i. Load the equation into the Y= menu of our graphing calculator and adjust the WINDOW parameters so that both turning points are visible in the viewing window. ii. Make a reasonable cop of the graph in the viewing window on our homework paper. Label and scale each ais with min, ma, min, and ma, then label the graph with its equation. Remember to draw all lines with a ruler. Perform each of the following tasks for the equations in Eercises i. Load the equation into the Y= menu. Adjust the WINDOW parameters until ou think all important behavior ( turning points, etc.) is visible in the viewing window. Note: This is more difficult than it sounds, particularl when we have no advance notion of what the graph might look like. However, eperiment with several settings until ou discover the settings that ehibit the most important behavior. ii. Cop the image on the screen onto our homework paper. Label and scale each ais with min, ma, min, and ma. Label the graph with its equation. 19. f() = f() = f() = f() = f() = f() = f() = f() =

3 Section 2.2 The Graph of a Function 2.2 Solutions 1. Evaluate the function f() = at 2, 1, 0, and 1. f( 2) = 2( 2) + 1 = 3 f( 1) = 2( 1) + 1 = 1 f(0) = 2(0) + 1 = 1 f(1) = 2(1) + 1 = 3 Place these results in table (a) and plot them as shown in (b). There is enough evidence here to intuit that the graph of f is the line shown in (b). 5 f()=2+1 f() = (, f()) 2 3 ( 2, 3) 1 1 ( 1, 1) 0 1 (0, 1) 1 3 (1, 3) 5 (a) (b) 3. Evaluate the function f() = 3 (1/2) at = 2, 0, 2, and 4. f( 2) = 3 (1/2)( 2) = 4 f(0) = 3 (1/2)(0) = 3 f(2) = 3 (1/2)(2) = 2 f(4) = 3 (1/2)(4) = 1 Place these results in table (a) and plot them as shown in (b). There is enough evidence here to intuit that the graph of f is the line shown in (b).

4 Chapter 2 Functions f()=3 /2 5 f() = 3 /2 (, f()) 2 4 ( 2, 4) 0 3 (0, 3) 2 2 (2, 2) 4 1 (4, 1) 5 (a) (b) 5. Evaluate f() = 2 2 at = 3, 2, 1, 0, 1, 2, and 3. f( 3) = ( 3) 2 2 = 7 f( 2) = ( 2) 2 2 = 2 f( 1) = ( 1) 2 2 = 1 f(0) = (0) 2 2 = 2 f(1) = (1) 2 2 = 1 f(2) = (2) 2 2 = 2 f(3) = (3) 2 2 = 7 Place these results in table (a) and plot them as shown in (b). There is enough evidence here to intuit that the graph of f is the curve shown in (b). f() = 2 2 (, f()) 3 7 ( 3, 7) 2 2 ( 2, 2) 1 1 ( 1, 1) 0 2 (0, 2) 1 1 (1, 1) 2 2 (2, 2) 3 7 (3, 7) (a) 10 f()= 2 2 (b) Evaluate f() = 2 /2 6 at = 4, 2, 0, 2, and 4. f( 4) = ( 4) 2 /2 6 = 2 f( 2) = ( 2) 2 /2 6 = 4 f(0) = (0) 2 /2 6 = 6 f(2) = (2) 2 /2 6 = 4 f(4) = (4) 2 /2 6 = 2

5 Section 2.2 The Graph of a Function Place these results in table (a) and plot them as shown in (b). There is enough evidence here to intuit that the graph of f is the curve shown in (b). f() = 2 /2 6 (, f()) 4 2 ( 4, 2) 2 4 ( 2, 4) 0 6 (0, 6) 2 4 (2, 4) 4 2 (4, 2) 10 f()= 2 / (a) (b) 9. Load the function f() = 4 into Y1 as shown in (a). Select TBLSET, then highlight ASK for the independent variable and press ENTER (see (b)). It doesn t matter what is entered for TblStart or Tbl. Select TABLE and enter the -values 4, 5, 6, 7, 8, 9, and 10, as shown in (c). Plot the points in table (c) in. This is enough to intuit that the graph of f is the curve shown in. 10 f()= 4 10

6 Chapter 2 Functions 11. Load the function f() = 2 30 into Y1 as shown in (a). Adjust the WINDOW parameters as shown in (b). Push the GRAPH button to obtain the graph of f in (c). Cop the image onto our homework as shown in. 50 f()= Load the function f() = into Y1 as shown in (a). Adjust the WINDOW parameters as shown in (b). Push the GRAPH button to obtain the graph of f in (c). Cop the image onto our homework as shown in.

7 Section 2.2 The Graph of a Function f()= Load the function f() = into Y1 as shown in (a). Adjust the WINDOW parameters as shown in (b). Push the GRAPH button to obtain the graph of f in (c). Cop the image onto our homework as shown in. 100 f()=

8 Chapter 2 Functions 17. Load the function f() = into Y1 as shown in (a). Adjust the WINDOW parameters as shown in (b). Push the GRAPH button to obtain the graph of f in (c). Cop the image onto our homework as shown in f()= Load the function f() = into Y1 as shown in (a). Adjust the WINDOW parameters as shown in (b). Push the GRAPH button to obtain the graph of f in (c). Cop the image onto our homework as shown in.

9 Section 2.2 The Graph of a Function 600 f()= Load the function f() = into Y1 as shown in (a). Adjust the WINDOW parameters as shown in (b). Push the GRAPH button to obtain the graph of f in (c). Cop the image onto our homework as shown in f()=

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