To find the domain and range of the function shown in the graph:

Domain:

• The domain refers to all possible values of $x$, which in this case is "Time (days)".
• From the graph, the time starts at $0$ days and ends at $90$ days.
• Therefore, the domain is: $\{x \mid 0 \leq x \leq 90\}$

Range:

• The range refers to all possible values of $y$, which is the "Length of the road (kilometers)".
• From the graph, the length starts at about $60$ kilometers and ends at about $150$ kilometers.
• Therefore, the range is: $\{y \mid 60 \leq y \leq 150\}$

Would you like further details or have any other questions?

Here are 5 related questions to explore:

1. How would the domain and range change if the graph extended to 120 days?
2. What is the significance of the slope of this graph?
3. How do you determine the domain and range from a non-linear graph?
4. If the road construction rate increased, how would this affect the graph?
5. How would you write the function that represents this graph?

Tip: When identifying domain and range, look at the start and end values of $x$ (for domain) and $y$ (for range) on the graph.