The graph we saw earlier shows a new journey taken by Wile E. Coyote. a. Write a story that could be represented by that graph. (Remember that graph shows Wile E.'s distance from a starting point, such as his cave. It is not a graph of the total distance traveled.) b. Construct a new graph of the relationship represented in the given graph. This time, graph the total distance traveled over time.

Consider the following situation:

• Wile E. Coyote leaves his cave walking at a slow, constant rate. He walks to the edge of a cliff. He is planning to build a catapult that will hit Road Runner by launching a large boulder. Just as Wile E. Coyote reaches the cliff, he remembers that he left the large rubber band for the catapult back in his cave. He turns around and walks back to his cave at the same pace as before. It takes him several minutes in the cave to find the large rubber band for the catapult. He realizes that he had better hurry so he starts running (at a constant speed). About halfway to the cliff, he remembers that he also left the boulder at home. He turns around and runs home at an even faster (yet constant) speed. a. Graph the relationship between Wile E. Coyote's total distance traveled and time. b. Create a second graph, this time graphing Wile E.'s position (i.e., his distance from the cave) and time. c. Compare the two graphs. How are they alike? How are they different?

This graph represents Pat's walk from home to a snack shop, then to the library, and then back home.

a. In the graph, what would suggest that Pat forgot her money?

b. During which part of the walk did Pat walk the farthest? How do you know?

c. Which part of the trip took Pat the longest time? How do you know?

d. In which part of the trip did Pat walk the fastest? Explain how you know, not in terms of slope, but in terms of distance and time considerations.

e. Can you tell whether Pat's walk involved any steep hills? Explain.

a. In a distance-time graph of Wile E., how can you tell when Wile E. has stopped?

b. In a speed-time graph of Wile E., how can you tell when Wile E. has stopped?

c. ln a position-time graph of Wile E.'s distance from his cave, how can you tell when Wile E. has stopped?

Make a distance-time graph and a speed-time graph for the following story. Align them so that the pieces can be compared.

Wile E. leaves his cave and trots steadily out to the spring. He continues on more slowly but at a steady pace, sniffing the ground as he goes. One smell was particularly interesting, so he stopped for a long sniff. He recognizes the Road Runner's smell and continues on, running fast. When he gets to the edge of a cliff, he stops and looks around. But the Road Runner is not in sight.

The graph we saw earlier shows a new journey taken by Wile E. Coyote. a. Write a story that could be represented by this graph. (Remember that this graph shows Wile E.'s distance from his cave. It is not a graph of the total distance traveled. The letters in the graph allow a discussion, but you do not need to mention them in your story.) b. Construct a new graph of the relationship represented in the graph on the previous page. But this time, graph the total distance traveled over time.

Martina fills a bathtub with 80 gallons of water. When she pulls the drain plug, the amount of water left in the tub after x minutes is modeled by the equation y = -9.5x + 80. Which of the following is the best interpretation of the slope of this line?

A maximum capacity of the bathtub

B number of gallons drained each minute

C time needed to completely drain the tub

D number of gallons drained in 5 minutes

Which of the following equations represents a proportional relationship? Select Yes or No. A y=3x Yes No B y=(1/2)x+1 Yes No C y=3/x Yes No D y=x/3 Yes No

Consider the following situation:

• Wile E. wakes up and, after eating breakfast, leaves his cave and trots out to the spring for a drink of water. As he slowly saunters back toward the cave, about halfway he thinks he sees Road Runner on the other side of the spring, so he runs fast in that direction. When he gets to the spring, however, he realizes that he was incorrect, so he slowly saunters back to the cave. a. Graph the relationship between Wile E.'s total distance traveled and time. Start the graph at the time when Wile E. wakes up. b. Make a second graph, this time graphing Wile E.'s position (i.e., his distance from the cave) and time. Use the same scale as in part (a) and put part (b) right under part (a) to allow an easy comparison for part (c). c. Compare the two graphs. How are they alike? How are they different?

Why does it make sense to say that both of these students have the "graph as picture" misconception?

In Exercise we saw earlier, the graphs for walkers $\mathbf{b}$ and c cross. What does that mean, if the walkers started at the same time (with different motion detectors)?

What does a speed-time graph like the one below mean?

With an initial deposit of $\$100$, and an interest rate of $8\%$, the balance in a bank account after t years is $f(t) = 100(1.08)^t$ dollars.

(a) What are the units of the rate of change of $f(t)$?

(b) Find the average rate of change over $[0, 0.5]$ and $[0, 1]$.

(c) Estimate the instantaneous rate of change at $t = 0.5$ by computing the average rate of change over intervals to the left and right of $t = 0.5$.

The given graph represents Susan's distance from home, over time, for her trip from her house to the grocery store.

During which segment of her journey did Susan take the longest? How do you know?