The image contains a worksheet focusing on functions and continuity, specifically dealing with the concepts of domain, range, and whether a given relation is a function. Below is a breakdown of the tasks:

Problems and Instructions on the Worksheet:

1. Identifying Functions and Their Domains/Ranges:

   • Problems 1 & 2:
     • These involve identifying if a given mapping is a function and determining the domain and range.
   • Problems 3 & 4:
     • These involve determining if a graph represents a function and identifying the domain and range.

2. Graphing Relations or Functions:

   • Problems 5 & 6:
     • Given a set of ordered pairs, graph the relation, then identify the domain and range, and decide if the relation is a function.

3. Composite Functions and Range Identification:

   • Problems 7 & 8:
     • Here, the task is to evaluate composite functions and determine the domain and range.

Would you like help solving a specific problem, or should I go through each one in detail?

Questions for Further Exploration:

1. What is the difference between a function and a general relation?
2. How can you determine the domain and range from a set of ordered pairs?
3. What is the vertical line test, and how does it determine if a graph represents a function?
4. Can the domain of a function include negative values, and under what conditions?
5. How do you find the composite function $(f \circ g)(x)$ given $f(x)$ and $g(x)$?

Tip:

When evaluating whether a graph represents a function, use the vertical line test: if any vertical line crosses the graph more than once, the graph does not represent a function.