Verify divisibility, additivity, and convexity

In summary, the three two-dimensional graphs asked about their divisibility, additivity, and convexity qualities. Divisibility refers to how easily a good can be divided into smaller units, additivity refers to the ability to combine two or more goods, and convexity refers to the shape of the graph.
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Homework Statement



There are three two-dimensional graphs and asked about their divisibility, additivity, and convexity qualities.

I know how to distinguish convexity - when all the points on the straight line between any two points of the set are also contained in the set.

But I have been struggling to understand how to recognize graph's divisibility and additivity. Divisibility implies that goods are infinitely divisible. Additivity means that it's possible to add consumption bundles.
Can you help please?

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Homework EquationsN/AThe Attempt at a SolutionDivisibility: This refers to how easily a good can be divided into smaller units. In the context of the graphs, it would refer to how easy it is to identify a specific point on the graph. In general, a graph with a lot of points and curves will be more divisible than one with fewer points and curves.Additivity: This refers to the ability to combine two or more goods in order to create a single, larger bundle of goods. In the context of these graphs, it would refer to the ability to take two or more points on the graph and add them together in order to create a single, larger bundle of points. Convexity: This refers to the shape of the graph. A convex graph will have all of its points connected in a smooth, curved line. A non-convex graph will have points that are not connected in a smooth, curved line.
 

FAQ: Verify divisibility, additivity, and convexity

What is divisibility?

Divisibility is the property of being able to divide one number by another without having any remainder. In other words, if a number is divisible by another number, it can be divided evenly without leaving any leftover pieces.

How do you verify divisibility?

To verify divisibility, you can use a variety of methods depending on the numbers involved. For example, to check if a number is divisible by 2, you can simply see if it is an even number. For larger numbers, you can use divisibility rules, such as the rule for 3 (if the sum of the digits is divisible by 3, the number is also divisible by 3).

3. What does it mean for a function to be additive?

An additive function is one that follows the property of additivity, which means that if you add two inputs together, the output will be the same as if you had applied the function to each input separately and then added the results. In other words, the function's output is the sum of its inputs.

4. How do you verify additivity in a function?

You can verify additivity in a function by checking if it follows the definition mentioned above. This means testing the function with different inputs and seeing if the output is the same as if you had applied the function separately to each input and then added the results. If the outputs are not the same, the function is not additive.

5. What is convexity in mathematics?

In mathematics, convexity is a property of a function or a set that describes the shape of its graph. A function is convex if its graph is always below the line segment connecting any two points on the graph. In other words, the function does not dip below this line, making it appear "curved" in a certain way.

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