The problem asks for the domain and range of the function shown in the graph, using inequality notation.

Step 1: Determine the Domain

The domain refers to the set of all possible input values (x-values) that the function can take. From the graph:

• The function appears to start at $x = -2$ and end at $x = 3$.
• The function is defined for every value of $x$ between $-2$ and $3$, inclusive.

Thus, the domain in inequality notation is: $-2 \leq x \leq 3$

Step 2: Determine the Range

The range refers to the set of all possible output values (y-values) that the function can produce. From the graph:

• The lowest point on the graph appears to be $y = -1$.
• The highest point on the graph appears to be $y = 2$.

Therefore, the range in inequality notation is: $-1 \leq y \leq 2$

Final Answer:

• Domain: $-2 \leq x \leq 3$
• Range: $-1 \leq y \leq 2$

Would you like more details, or do you have any further questions?

Here are five related questions:

1. How would the domain and range change if the graph was shifted 2 units up?
2. What are the domain and range for a function that is defined for all real numbers?
3. How do you find the domain of a function that includes a square root?
4. What is the range of a quadratic function?
5. How does the range of a function change if you multiply the function by a negative number?

Tip: Always check both the minimum and maximum values on the graph when determining the range of a function.