To determine which of the relations in the given graphs are functions, we apply the vertical line test. A relation is a function if no vertical line intersects the graph more than once.

Analyzing each graph:

• Graph I: This graph shows a curve. Applying the vertical line test, any vertical line will intersect the graph only once. Therefore, this relation is a function.
• Graph II: This is a circle. A vertical line drawn through the middle of the circle will intersect the graph at two points. Therefore, this relation is not a function.
• Graph III: This graph is a straight line. Any vertical line will intersect the graph at exactly one point. Therefore, this relation is a function.
• Graph IV: This graph consists of distinct points that are horizontally aligned. A vertical line can only pass through one point at a time. Therefore, this relation is a function.

Conclusion:

The relations that are functions are I, III, and IV.

Thus, the correct answer is D) I, III, and IV only.

Would you like more details or have any further questions?

Here are five related questions:

1. How does the vertical line test help determine if a relation is a function?
2. What would happen if Graph IV had points overlapping vertically?
3. Can you provide examples of real-world scenarios that represent functions?
4. How can we determine if a relation is not a function using its equation?
5. What are some examples of common relations that are not functions?

Tip: Always remember the vertical line test is a quick and effective way to check if a graph represents a function.