Looking at the image you provided, it appears that the question asks whether the given graphs represent functions ("Handelt es sich bei den folgenden Darstellungen um Graphen einer Funktion?"). Here's an analysis of each graph:

1. Top left (dots on a coordinate plane):

   • This does not represent a function. A function must pass the vertical line test, meaning for every $x$-value, there should be at most one $y$-value. Here, there are multiple points with the same $x$-coordinate but different $y$-coordinates.

2. Top right (partially connected curve):

   • This does not represent a function either. At $x = 0$, there are two different $y$-values, which violates the definition of a function (fails the vertical line test).

3. Bottom left (parabola opening upwards):

   • This is a function. For every $x$-value, there is exactly one $y$-value. This graph passes the vertical line test.

4. Bottom right (hourglass-like shape):

   • This does not represent a function. There are multiple $y$-values for the same $x$-value, which violates the definition of a function.

So, the correct answer should be:

• First graph: kein Graph
• Second graph: kein Graph
• Third graph: Graph
• Fourth graph: kein Graph

Would you like more details or have any other questions?

Here are 5 related questions to consider:

1. What is the vertical line test, and why is it used to determine if a graph represents a function?
2. Can a function have more than one $x$-value corresponding to the same $y$-value?
3. What are the characteristics of a one-to-one function?
4. How can a piecewise function be represented graphically?
5. How do graphs of quadratic functions (like the parabola shown) behave in general?

Tip: When checking whether a graph is a function, imagine drawing vertical lines across the entire graph—if any line crosses the graph at more than one point, it's not a function.