Graphs of Non-Linear Functions

Transcription

1 Classwork Exploratory Challenge 1. Plot a graphical representation of the distance of the ball down a ramp over time. Discussion 2. Did everyone s graph have the same shape? What differences were there? 3. What would have helped you draw a more accurate graph? S.13

2 4. The table below gives the data that one student recorded by pausing the ball rolling video and recording the number of seconds and the distance the front of the ball has rolled. Use the data to create a graph. Time in Seconds Distance in centimeters Ball Rolls Down a Ramp Distance in Centimeters Time in Seconds Did the new graph surprise you? What does this mean in terms of the speed of the ball? 6. A. Determine the average rate of change from 10 seconds to 12 seconds. B. Determine the average rate of change from 12 seconds to 14 seconds. C. Determine the average rate of change from 14 seconds to 16 seconds. In Lesson 1, the piecewise functions were all made up of lines. Lines that increased, decreased or were constant. In this lesson, you will see that sometimes graphs are composed of curves, as well as, lines. S.14

3 7. Watch the following graphing story: Elevation vs. Time #4 [ The video is of a man hopping up and down several times at three different heights (first, five mediumsized jumps immediately followed by three large jumps, a slight pause, and then 11 very quick small jumps). A. What object in the video can be used to estimate the height of the man s jump? What is your estimate of the object s height? B. Draw your own graph for this graphing story. Label your xx-axis and yy-axis appropriately and give a title for your graph. S.15

4 Lesson Summary The curves you drew in this lessons are exponential and quadratic curves. You ll learn more about these curves in Modules 3 and 4. Exponential Curves Exponential curves may start close to the y-axis and then they grow more and more rapidly or may start far from the y-axis and decrease rapidly. Quadratic Curves The graph of a quadratic function is a parabola. It is a U-shaped curve, but sometimes we only see half of this curve in real-life situations. You often see these curves upside down. S.16

5 Homework Problem Set 1. Professor Splash set a world record by doing a belly flop from 36 feet in the air into a kiddie pool with 12 inches of water. His data was recorded by someone at the bottom of the tower. A. Graph the data to see the curve that represents his distance from the ground over time. Time in Seconds Elevation in Feet B. Which type of curve (linear, quadratic, exponential) is the best description of this graph? Why? C. What is the y-intercept and what does it represent? D. What is the x-intercept and what does it represent? S.17

6 2. Use the table below to answer the following questions. A. Plot the points (xx, yy) in this table on a graph (except when xx is 5). B. The yy-values in the table follow a regular pattern that can be discovered by computing the differences of consecutive yy-values. Find the pattern and use it to find the yy-value when xx is 5. C. Plot the point you found in part (b). Draw a curve through the points in your graph. Does the graph go through the point you plotted? D. How is this graph similar to the graphs you drew in this lesson? How is it different? S.18

7 3. Bacteria reproduce quite rapidly. The pictures below show the growth of the bacteria every 20 minutes. A. Use the table to graph the growth of the bacteria. Time in minutes Number of Bacteria Number of Bacteria Bacteria Growth Time in Minutes B. How many bacteria should they expect to have after 140 minutes if the bacteria continue to grow at this rate? C. Can we tell what will happen at 10 minutes? Explain your thinking. D. Will this curve ever be perfectly vertical? Explain your thinking. E. John says we shouldn t connect the points on the graph. Do you agree with him? Explain. S.19

8 4. A ramp is made in the shape of a right triangle using the dimensions described in the picture below. The ramp length is 10 ft. from the top of the ramp to the bottom, and the horizontal width of the ramp is 9.25 ft. A ball is released at the top of the ramp and takes 1.6 sec. to roll from the top of the ramp to the bottom. Find each answer below to the nearest 0.1 ft sec. A. Find the average speed of the ball over the 1.6 sec. B. Find the average rate of horizontal change of the ball over the 1.6 sec. C. Find the average rate of vertical change of the ball over the 1.6 sec. D. What relationship do you think holds for the values of the three average speeds you found in parts A, B and C? (Hint: Use the Pythagorean Theorem.) S.20