The image you uploaded contains several mathematical problems involving functions, relations, and graphs. Let's analyze and solve each problem shown:

1. Problem 7:

   • Given: Two functions $f$ and $g$.
   • Task: Write the inverse of $g$ as a set of ordered pairs.
   • Solution: For each ordered pair in $g$, reverse the coordinates to form the inverse $g^{-1}$.

2. Problem 8:

   • Task: Determine whether the given relation is a function.
   • Solution: A relation is a function if each input (x-value) is associated with exactly one output (y-value). Review the relation to determine if this condition is satisfied.

3. Problem 9:

   • Task: Determine if the given graph represents a function.
   • Solution: Use the Vertical Line Test. If any vertical line intersects the graph at more than one point, the graph does not represent a function.

4. Problem 10:

   • Task: Determine if the graph represents a function and state the domain and range.
   • Solution: Again, apply the Vertical Line Test to determine if it is a function. The domain is the set of all possible x-values, and the range is the set of all possible y-values that the graph covers.

5. Problem 11:

   • Task: Determine if the equation defines y as a function of x.
   • Solution: Rearrange the equation and apply the definition of a function. For every x-value, there should be only one corresponding y-value.

Would you like detailed solutions or explanations for any specific problem? Let me know if you have any questions or need further assistance.

Here are five questions related to the concepts in the problems:

1. What are the steps to find the inverse of a function given as a set of ordered pairs?
2. How can you verify whether a set of points represents a function?
3. What is the Vertical Line Test, and how is it used to determine if a graph represents a function?
4. How do you determine the domain and range of a function from its graph?
5. What are the common methods to verify if an equation defines y as a function of x?

Tip: Always remember that a function has only one output for each input. This is key in determining whether a relation, graph, or equation defines a function.