To determine whether the relation given is a function, we need to check if each input (the first element of each ordered pair) maps to only one unique output (the second element of each ordered pair). A relation is a function if no input (x-value) repeats with different outputs.

The given relation is: $\{(1,4), (3,7), (4,1), (1,1)\}$

Let's examine the x-values (inputs):

• For $x = 1$, there are two outputs: 4 and 1.
• For $x = 3$, there is one output: 7.
• For $x = 4$, there is one output: 1.

Since $x = 1$ is associated with two different outputs (4 and 1), this violates the definition of a function, which requires each input to have exactly one output. Therefore, this relation is not a function.

Would you like more details or have any further questions?

Here are some related questions to explore:

1. What conditions must a relation satisfy to be classified as a function?
2. How can we represent functions visually on a graph?
3. What are some real-world examples of functions and non-functions?
4. How does the vertical line test help in identifying functions?
5. Can a function have two inputs with the same output?

Tip: To quickly check if a relation is a function, look for repeated x-values with different y-values. If found, the relation is not a function.