Review 5 Symbolic Graphical Interplay Name 5.1 Key Features on Graphs Per Date
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1 3 1. Graph the function y = a. Circle the -intercept. b. Place an on the y-intercept.. Given the linear function with slope ½ and a y-intercept of -: Draw a line on the coordinate grid to graph the function. Place a point on the line representing the -intercept of the function. Page 1
2 3. A linear function includes the point (, 6), as indicated on the coordinate grid below, and has slope 3. Mark with an the y-intercept of the line. Mark with a circle the -intercept of the line Given the function y = + 1, Draw a graph on the coordinate grid below that represents the graph of the function. Mark with a circle the point that represents the y-intercept of the function. Mark with a square each point that represents an -intercept of the function. Page
3 5. Given the function y = + + 3, Place a point on the coordinate grid to show each -intercept of the function. Place a point on the coordinate grid to show the maimum value of the function. 6. Given the function y = ( + ) 18, Place a point on the coordinate grid to show each -intercept of the function. Page 3
4 7. Given the function y = + 3, Place a point on the coordinate grid to show each -intercept of the function. Bonus: Graph the function Given the function y = 8+ 1, Place a point on the coordinate grid to show the -intercept of the function. Bonus: Graph the function. Page 4
5 9. Given the function 3 y 6 = +, Place a point on the coordinate grid to show each -intercept of the function. Bonus: Graph the function Given the function y = and that (1,0) is a point on the graph of this function, Place a point on the coordinate grid to show each -intercept of the function. Bonus: Graph the function. Page 5
6 11. Given the function = 1and that (-1,0) is a point on the graph of this function, 3 y Place a point on the coordinate grid to show each -intercept of the function. Bonus: Graph the function. The zeros are at 1 ± 5 1.6, Given the function y = 3, Place a point on the coordinate grid to show the -intercept of the function. Bonus: Graph the function. y-intercept is at (0, -.75), -intercept is at log log Page 6
7 13. Given the function 1 =, y e + 1 Place a point on the coordinate grid to show the -intercept of the function. Bonus: Graph the function. y-intercept at (0, e 1) int at (-1, 0) 14. Given the function y = 4log( + 5), Place a point on the coordinate grid to show the -intercept of the function. Bonus: Graph the function. y-intercept at (0, 4log5), -intercept at (-4, 0) Page 7
8 15. Given the function y = 5ln( + 3), Place a point on the coordinate grid to show the -intercept of the function. Bonus: Graph the function. y-intercept at (0, 5ln3), -intercept at (-, 0) 16. Given the function for < 3 = 4 3 1, y for + 3 for > 1 Place four points on the coordinate grid to show the values of y when = -3, -4, 0, and. Bonus: Graph the function. Page 8
9 5. Function Properties and Behavior Per Date 1. For each function in the table below place an in the cell that describes the function s end behavior for large positive values of. Function y = = = + 5 = = = = e f( ) = log( + 3) 1 = 7 = + 10 = = = ( 3 1 )( + 5 ) 10 for 0 = + 1 for > 0 = ln( ) Page 9
10 5. Function Properties and Behavior Per Date. Enter the equation for the line of symmetry for the function f defined by = = 3. Enter the equation for the line of symmetry for the function f defined by 11 = = 6 4. Enter the equation for the line of symmetry for the function f defined by = = 3 5. Koa stands on the top of a 4-story building and throws a ball up in the air. The ball s height (h) in feet with respect to time (t) in seconds can be modeled by the quadratic function, ht () = 16t + 3t+ 48. a. How long does it take the ball to reach its maimum height? 1 second b. What is the maimum height the ball attains? 64 ft. c. How long does it take the ball to hit the ground below? 3 seconds 6. Determine whether each function represents eponential growth or decay and place an in the appropriate column for each function. In the last column enter the growth/decay rate over one unit. Round decimal responses to decimal places. Function Growth Decay Rate ( ) f( ) = / 3 /3 ( ) f( ) = 4/ 3 4/3 ( ) f( ) = 3/ 9/4 ( ) f( ) = 4/ ( 1 014) 10 f( ) = ( ) f( ) = 31/.7 Page 10
11 5. Function Properties and Behavior Per Date 7. What is the y-intercept for the function f defined by 3 =? Rewrite f in standard eponential form = a b. The y-intercept is (0, 1/9). = 3 = 3 3 = In which interval(s) on the -ais are the functions f and g both increasing, where f is defined by = ( 1) + 6 and g is defined by g ( ) = ( + 1)( + 3)? Mark the interval(s) on the number line below. 9. Given the graph of the quadratic function f below and g ( ) = ( 1)( 4), select whether each statement is True or False. Statement True False The minimum value for f() is greater than the minimum value for g(). The value of when f() is at its minimum is greater than the value of when g() is at its minimum. Both -intercepts of g() occur when is less than zero. The line of symmetry of f() is = -. Page 11
12 5. Function Properties and Behavior Per Date 10. Select the appropriate bo to indicate the match of each table to its equation. Table A f() Table B f() Table C f() Equation Table A Table B Table C = = = Page 1
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