Question

analysis of graphs and rate of change
1 complete the graph for tortoise by providing labels for the axes and a title.
a what does the graph show?
b how would you label the x - and y - axes?
2 what could it mean when the graph is a straight line? give two examples.
3 what does it mean when the graph increases steeply? gradually?
4 add an animal to the race and describe its progress. sketch its graph

Explanation:

Step1: Analyze question a

The graph likely shows the progress of the tortoise over a variable. Since it's related to a race - like scenario, it could show distance traveled over time.

Step2: Answer question a

The graph shows the distance the tortoise has traveled over time.

Step3: Analyze question b

The x - axis is usually the independent variable and the y - axis is the dependent variable. In this case, time is independent and distance is dependent.

Step4: Answer question b

The x - axis could be labeled "Time (minutes/hours etc.)" and the y - axis could be labeled "Distance (meters/kilometers etc.)"

Step5: Analyze question 2

A straight - line graph means a constant rate of change.

Step6: Answer question 2

Example 1: A car moving at a constant speed. The distance - time graph of the car is a straight line as the speed (rate of change of distance with respect to time) is constant. Example 2: A person walking at a steady pace. The distance they cover over time will result in a straight - line graph.

Step7: Analyze question 3

A steep increase means a large change in the y - variable for a small change in the x - variable. A gradual increase means a small change in the y - variable for a change in the x - variable.

Step8: Answer question 3

When the graph increases steeply, it means the tortoise is covering a large distance in a short time (e.g., it has a high speed). When the graph increases gradually, it means the tortoise is covering a small distance in a given time (e.g., it has a low speed).

Step9: Analyze question 4

Let's add a hare. The hare starts fast, then stops to rest. Its graph would start with a steep upward slope (showing fast progress), then a horizontal line (showing it's not moving while resting), and then another upward slope if it starts moving again.

Step10: Sketch for question 4

Draw a graph with the x - axis labeled "Time" and the y - axis labeled "Distance". First, draw a steep upward - sloping line for a short time interval to represent the hare's fast start. Then draw a horizontal line to represent the resting period. Finally, draw another upward - sloping line (less steep than the first) if it resumes running.

Answer:

a. The graph shows the distance the tortoise has traveled over time.
b. x - axis: "Time (minutes/hours etc.)", y - axis: "Distance (meters/kilometers etc.)"

1. Example 1: A car moving at a constant speed. Example 2: A person walking at a steady pace.
2. Steep increase: large distance covered in short time (high speed). Gradual increase: small distance covered in given time (low speed).
3. Added a hare. Graph has a steep upward slope at first, then a horizontal line, and then another upward slope if it resumes running.