For Questions 1-15, NO CALCULATOR!

Transcription

1 For Questions 1-15, NO CALCULATOR! 1. Identify the y-intercept: Identify the vertex: 2. The revenue, R(x), generated by an increase in price of x dollars for an item is represented by the equation Identify whether the function has a maximum or minimum: State the maximum or minimum: Identify y-intercept: 3. Given Identify the x-intercepts: Determine the y-intercept: Determine the vertex:

2 4. The height of a golfer s ball is given by the equation, where y represents the height in feet and t represents the time in seconds. Graph the function. What is the vertex? What does the maximum value mean in the context of the problem? 5. What is the value of x that minimizes or maximizes the function? For what values of x is the function increasing? Decreasing? A function has a maximum value of 6.8 and x-intercepts of 11.5 and Maximum or Minimum at: Increasing: Decreasing: 6. Determine whether the function is even, odd, or neither. Explain why.

3 7. You are practicing punting a football before football tryouts. Your kicked the ball from the ground represented by the point (0,0), and the path of the ball is parabolic. The table below represents the height of the ball seconds after being kicked. Determine at what times the height of the ball is increasing and decreasing and when it hits it ultimate height. Time (seconds) Ball height (feet) For each function, identify the y-intercept, vertex, and maximum or minimum. Then, sketch a graph of the function. Identify the y-intercept: Identify the vertex: Identify whether the function has a maximum or minimum: State the maximum or minimum: Sketch the graph:

4 9. Calculate the average rate of change for each function listed below between and a. b. c. x y Is the average rate of change greater between and or between and?

5 11. A zoo increased the lengths of both sides of its monkey park by the same amount. As a result, the monkey park is 500 feet by 600 feet. Define a function for each side length of the original park before it was enlarged and use those functions to build an area function. 12. An amusement park is building a steel roller coaster with a section so steep that when the roller coaster descends the riders feel almost weightless. The section is modeled by a concave down parabola. In this section, the roller coaster will start its ascent at (0, 0), reach the peak at 60 feet above the starting point, and return to its starting height at a horizontal distance of 240 feet from the start. What are the coordinates of the vertex and the x-intercepts? 13. Let and 1. Find. 2. Find. 3. Find. 4. Find. State any restrictions on the domain. 14. What is the critical point of? 15. What is the minimum of the graph?

6 For Questions 16-22, you MAY use a calculator. 16. For the following function, find the values of x for where it is increasing and decreasing. Increasing: Decreasing: 17. Increasing: Decreasing: Maximum or minimum value: x-intercepts: Even, odd, or neither (show work): 18. Use graphing technology to determine the domain of each function. a. b. 19. Graph the function. Note the domain, range, and any critical points. Domain: Range: Critical Point(s):

7 20. Graph the functions and Describe any similarities and differences between the graphs, including domain, range, and critical points. Similarities: Differences: Domain: Range: Critical Point(s): 21. Graph the function. Note the domain, range, and any critical points. Domain: Range: Critical Points: 22. The path of a rock launched from a slingshot can be described by the equation, where f(x) is the height of the rock and x is the number of seconds that have passed since the slingshot s band was released. Which of the following points shows the extremum for the function? a. (0, 3) b. (3, 12) c. (2, 11) d. ( 6, 3)