Question

The distance, y, in centimeters, of an ant from a hole in the tree for a certain amount of time, x, in seconds, is shown in the graph: A graph titled Motion of Ant is shown. The graph shows time in seconds on the x-axis and the Distance from Hole in centimeters on the y-axis. The scale on the x-axis is shown from 0 to 6 at increments of 1, and the scale on the y-axis is shown from 0 to 18 at increments of 3. The graph has 3 straight lines. The first line is labeled K and joins ordered pairs 0, 0 and 2, 9. The second line is labeled L and joins ordered pairs 2, 9 and 5, 9. The third line is labeled M and joins ordered pairs 5, 9 and 7, 0. Part A: Is the graph linear or nonlinear? Explain your answer. (2 points) Part B: In which segments is the graph increasing, decreasing, and constant? (3 points) Part C: In your own words, describe the motion of the ant, as shown on the graph. (5 points)

Answer 1

Part A: the graph is nonlinear.

Part B:

The graph is increasing in the segment K

The graph is constant in the segment L

The graph is decreasing in the segment M

Part C:

We can see in the graph that the ant goes out from the hole at 0 seconds, and starts walking away from it. A 2 seconds stop moving at a distance of 9cm. Remains there for 3 seconds (5 in total since the ant leaves the hole), and starts moving toward the hole, and reaches it 7 seconds before leaving it.

Step-by-step explanation:

For the part A, a linear function is a function that shows a straigth line. Since this is a line created by segments, it's not a straigth line. Thus the graph is nonlinear.

In part B we need to lok at where the function is increasing, constant and decreaing. When the function is increasing, for each second that happens, the ant goes further away from the hole. When is constant, the distance from the hole remains the same. When is decreasing, the ant is each second that passes, closer to the hole.

We then ca see that:

• The graph is increasing in the segment K

,

• The graph is constant in the segment L

,

• The graph is decreasing in the segment M

Finally, in part C, we can see in the graph that the ant goes out from the hole at 0 seconds, and starts walking away from it. A 2 seconds stop moving at a distance of 9cm. Remains there for 3 seconds (5 in total since the ant leaves the hole), and starts moving toward the hole, and reaches it 7 seconds before leaving it.