The cheat sheet in your image covers the basics of functions and how to determine if a given relation is a function. Let me help break down and clarify the content shown:

Key Points from the Cheat Sheet:

1. Definition of a Function:

   • A function is a relationship where each input (denoted as $x$) has exactly one output (denoted as $y$).

2. How to Check if It's a Function:

   • Ordered Pairs & Tables:
     • Each $x$-value (input) must correspond with exactly one $y$-value (output).
     • Repeating $x$-values with different $y$-values indicate it's not a function.
   • Equations:
     • Analyze whether a single input $x$ results in more than one output $y$. If it does, it's not a function. Example provided is $y^2 = x$, which can produce ±$y$ values for the same $x$.
   • Graphs:
     • Apply the "Vertical Line Test": If any vertical line crosses the graph at more than one point, the relation is not a function.

Would you like further explanations or examples for any of these points?

Here are 5 related questions to expand your understanding:

1. What is an example of an equation that does not represent a function? Why?
2. How do you verify if a table of values represents a function?
3. What happens if two ordered pairs have the same $x$-value but different $y$-values?
4. Can a graph with a sharp bend or cusp still represent a function? Why or why not?
5. What is the mathematical definition of the vertical line test?

Tip: To confirm a relation is a function, always check that each input corresponds to only one unique output, either visually or algebraically!