Representation of Phenomena: Linking function properties to its representation

Let's first observe the X-axis which is representative of the weight. Locate 7 kg - and mark a point.

From this point, we'll draw a vertical line until we meet the straight line.

Let's now observe the Y-axis which is representative of the price.

We will draw a line from the point where we reached the X-axis to the straight line, towards the Y-axis and determine the price: 8 dollars.

Let's first observe the Y-axis which is representative of the price. Locate 9 dollars - and mark a point.

From this point, we'll draw a vertical line until we meet the straight line.

Now let's observe the X-axis which is representative of the quantity in kg.

We'll draw a line from the point where we reached the Y-axis to the straight line, towards the X-axis and determine the weight: 8 kg.

Let's look at the red line:

The X-axis shows us the quantity, we'll locate 7 kg and from it draw a vertical line to the line - mark a point.

From this point we'll draw a horizontal line to the Y-axis which shows the price and we'll see that 7 kg costs 8 NIS.

Let's look at the blue line:

The X-axis shows us the quantity, we'll locate 7 kg and from it draw a vertical line to the line - mark a point.

From this point we'll draw a horizontal line to the Y-axis which shows the price and we'll see that 7 kg costs 10 NIS.

Therefore it's better to buy at the red store, it's cheaper.

Let's begin by observing the blue line that represents the second container.

Note that it will be full at the point where it starts to become a continuous line.

Hence let's draw a vertical line from this point to the X-axis which marks the minutes.

We can observe that the line reaches 22, meaning the container will be full in 22 minutes.

The problem asks us to determine if the two cyclists meet after departing at different times. To solve this, we would analyze the functions or the possible graphical representation of their journey concerning time.

From the provided scenario, cyclist one starts at 4 and cyclist two at 5. Without specific speed and distance, the problem might hint at a graphical or conceptual analysis.

Upon examining this scenario, since no intersection of their paths was indicated (or given speeds and times to compute), we need to conclude based on the apparent description or plot.

Without specific data points indicating overlap or meeting times between the two cyclists, we assume the visual information presented suggests that they indeed do not encounter each other on their paths.

Therefore, the cyclists do not meet, confirming the conclusion as per the given choices.

Therefore, the solution to the problem is: The cyclists do not meet.

The graph suggests that Cyclist 1 takes a break starting at 6 o'clock, as indicated by the appearance of the red flat section starting at the marker for 6. Similarly, Cyclist 2 takes a break starting at 8 o'clock, identified from the blue flat section starting at the marker for 8.

Thus, the riders take their breaks at:

• Cyclist 1 - at 6
• Cyclist 2 - at 8

Therefore, the solution to the problem matches the given correct answer.

Conclusion: Cyclist 1 takes a break at $t = 6$, and Cyclist 2 takes a break at $t = 8$.

To solve this problem, we'll follow these steps:

• Identify the initial fees: According to the problem, Dany's initial fee is 700 dollars, Alex's is 200 dollars, and Jonathan's has no initial fee (0 dollars).
• Analyze the chart: On the chart, the y-intercept of a line represents the initial fee charged before calculating based on garden size.
• Match each line: The line with the highest y-intercept matches Dany's 700 dollars, the next (200 dollars) matches Alex, and the zero y-intercept matches Jonathan.

According to the analysis, the lines match the gardeners as follows:
$$I = Jonathan (no initial fee, line passing through the origin)
$$II = Alex (200 dollars y-intercept, moderate slope)
$$III = Dany (700 dollars y-intercept, highest slope)

Therefore, the solution to the problem is: I = Jonathan, II = Alex, III = Dany.