To find the domain and range of the function represented by the graph:

1. Domain:

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

• Observing the graph, the function starts at $x = -2$ and goes up to $x = 7$.
• There are no breaks in the graph within this interval, meaning the function is defined for all $x$ from $x = -2$ to $x = 7$.
• Therefore, the domain is: $\text{Domain} = [-2, 7]$

2. Range:

The range of a function is the set of all possible output values (y-values) that the function can produce.

• The lowest point on the graph is at $y = -2$ (when $x \approx -1.8$).
• The highest point on the graph is at $y = 6$ (when $x = 7$).
• The function takes all values from $y = -2$ to $y = 6$.
• Therefore, the range is: $\text{Range} = [-2, 6]$

Would you like more details on this, or do you have any other questions?

Follow-up Questions:

1. What happens to the domain and range if the function has vertical asymptotes?
2. How would the domain change if there were a hole in the graph at a certain x-value?
3. Can you find the intervals of increase and decrease for this function?
4. How does the range change if we apply a vertical shift to the function?
5. What is the significance of closed and open dots in defining the domain and range?

Tip:

Always check for any gaps, holes, or asymptotes in the graph to accurately determine the domain and range of a function.