The image you provided shows a graph of a line. To determine whether it represents a function, we can apply the vertical line test: if any vertical line intersects the graph at more than one point, the graph is not a function.

• In this case, each vertical line will only intersect the graph at one point. Therefore, the graph is a function.

Domain and Range:

1. Domain (the set of all possible $x$-values):

   • The line appears to extend infinitely in both directions horizontally, meaning that the function can take any $x$-value.
   • The domain is therefore all real numbers, which can be written as:
     $\text{Domain}: (-\infty, +\infty)$

2. Range (the set of all possible $y$-values):

   • Similarly, since the line extends infinitely vertically, the function can take any $y$-value as well.
   • The range is also all real numbers, written as:
     $\text{Range}: (-\infty, +\infty)$

Would you like to explore more about how to determine domain and range for different types of graphs, or do you need any other clarifications?

Additional Questions:

1. How do you perform the vertical line test on different types of graphs?
2. What is the definition of a function in mathematics?
3. How can you determine if a function is continuous or discrete?
4. How do domain and range change for quadratic or exponential functions?
5. What happens to the domain and range if we restrict the graph to certain regions?

Tip:

When determining the range of a function, always check how the graph behaves as $x$ approaches infinity or negative infinity.