The problem asks which of the given graphs represent functions. To determine if a graph represents a function, we can use the Vertical Line Test. This test states that if a vertical line passes through more than one point on the graph, then the graph is not a function.

Let’s evaluate each graph:

1. Top-left graph: This is a straight diagonal line. A vertical line will intersect this graph at exactly one point for any value of $x$, so it is a function.

2. Top-right graph: This is a curved line (possibly part of a quadratic function). A vertical line will only intersect the curve at one point for any value of $x$, so it is a function.

3. Bottom-left graph: This is a V-shaped graph (possibly an absolute value function). A vertical line will intersect the graph at only one point for each $x$-value, so it is a function.

4. Bottom-right graph: This is a wavy line. If you draw a vertical line, it can intersect the graph at more than one point for some $x$-values, so it is not a function.

Conclusion:

• The graphs that are functions are:
  • Top-left (diagonal line)
  • Top-right (curved line)
  • Bottom-left (V-shape)

Would you like more details on the Vertical Line Test or functions? Let me know!

Here are 5 related questions:

1. How does the vertical line test help in identifying functions?
2. Can all linear graphs be considered functions?
3. How would you define a function in mathematical terms?
4. What are the key differences between a function and a relation?
5. Are there exceptions to the Vertical Line Test for special types of functions?

Tip: When analyzing graphs, always remember that functions can only assign one output (y-value) for each input (x-value).