Representation of Phenomena: Linking function properties to its representation

Examples with solutions for Representation of Phenomena: Linking function properties to its representation

Exercise #1

The graph below depicts the price of apples relative to the quantity.

How many kg of apples can you buy for $9?

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Video Solution

Step-by-Step Solution

Let's look at the Y-axis which shows us the price data. 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 look at the X-axis which shows us 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.

Answer

8

Exercise #2

The graph below depicts the price of apples relative to the quantity.

What is the price of 7 kg of apples?

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Video Solution

Step-by-Step Solution

Let's look at the X-axis which shows us the weight. Locate 7 kg - and mark a point.

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

Now let's look at the Y-axis which shows us the price.

We'll 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.

Answer

8

Exercise #3

The graph below depicts the price of tomatoes as a function of quantity, with each line representing the prices at different shops.

Where is it cheaper to buy 7 kg of tomatoes?

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Video Solution

Step-by-Step Solution

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.

Answer

In the red shop

Exercise #4

There are two water containers. The first container is empty, whilst the second contains 48 liters of water.

After how many minutes will the second container be completely full?

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Step-by-Step Solution

Let's look at the blue line that represents the second container.

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

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

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

Answer

22 minutes

Exercise #5

A car leaves Madrid for Barcelona. During the journey, the driver has a break.

For how many hours did the driver rest?

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Video Solution

Answer

6