To determine the function's domain and range from the given graph:

1. Domain: The domain refers to the set of all possible $x$-values for which the function is defined. Observing the graph:

   • The function extends horizontally without breaks, covering all $x$-values.
   • Thus, the domain is $(-\infty, \infty)$.

2. Range: The range refers to the set of all possible $y$-values the function can take. Observing the graph:

   • The lowest value of $y$ is 3 (on the flat section of the graph at $x < -2$).
   • The highest value of $y$ is 7 (on the flat section of the graph at $x > 6$).
   • All $y$-values between 3 and 7 are covered.
   • Thus, the range is $[3, 7]$.

Correct Answer: A. Domain: $(-\infty, \infty)$, Range: $[3, 7]$.

Would you like a detailed explanation of how domain and range are analyzed? Let me know!

5 Related Questions:

1. What does it mean for a function to have an "infinite" domain?
2. How can you determine the range from a graph with breaks or gaps?
3. What happens to the domain and range if a function is transformed (e.g., shifted or stretched)?
4. How would the domain and range differ for discrete functions compared to continuous functions?
5. Why is the range restricted in this graph, and how is it affected by horizontal segments?

Tip:

When analyzing a graph for domain and range, always look for where the function starts and ends (if at all) along both the $x$- and $y$-axes.