Question 6 - Distance from Haifa Analysis

Question 6 - Truck from Haifa

Distance-Time Graph Analysis

A truck left Haifa. During the trip it stopped twice.
The graph below describes the distance from Haifa as a function of time elapsed since the start of the trip.

The Graph

The Table

b. During which time intervals did the truck not travel? Explain.

Choose the correct answer:

1 Between hour 0 and 1 and between hour 4 and 5

2 Between hour 1 and 2 and between hour 3 and 3.5 (because the graph is horizontal - the distance does not change)

3 Between hour 5 and 7 (because the graph is going down)

4 The truck traveled the entire time without stopping

c. Did the truck return to Haifa? Explain.

Choose the correct answer:

1 Yes, the truck returned to Haifa because at time x=7 the distance is y=0

2 No, the truck did not return because at the end it remained 100 km away

3 It cannot be determined from the graph

4 Yes, because it stopped twice along the way

d. What was the maximum distance from Haifa during the trip?

Choose the correct answer:

1 100 km

2 150 km

3 200 km

4 250 km

e. Is it possible that at two different times the distance from Haifa was the same?

Choose the correct answer:

1 Yes, because on the way there and on the way back the truck passed through the same distances

2 No, each time has a different distance

3 No, because it is a function

4 Only during the stops

f. Is y (the distance) a one-to-one function of x (the time)?

Choose the correct answer:

1 Yes, because each time corresponds to a unique distance

2 No, because there are distances that correspond to more than one time (e.g., 150 km on the way there and back)

3 Yes, because the graph goes up and down

4 Cannot be determined

Reminder: A one-to-one function is a function in which each y value corresponds to at most one x value. In other words: every horizontal line intersects the graph at most at one point.