The graph shows a function $f$ that has a distinct starting and ending point. To find the domain and range of this function using interval notation:

Domain

The domain represents the set of all possible $x$-values (input values) for which the function is defined. By inspecting the graph:

• The leftmost point of the graph occurs at $x = -3$.
• The rightmost point of the graph occurs at $x = 3$.

Thus, the domain of the function is: $[-3, 3]$

Range

The range represents the set of all possible $y$-values (output values) of the function. By inspecting the graph:

• The lowest point of the graph occurs at $y = 1$.
• The highest point of the graph occurs at $y = 5$.

Thus, the range of the function is: $[1, 5]$

So, the domain and range in interval notation are:

• Domain: $[ -3, 3 ]$
• Range: $[ 1, 5 ]$

Would you like further details or clarifications on any part of this?

Here are 5 related questions to explore:

1. What does it mean when a graph has a closed interval for its domain or range?
2. How would the domain change if the function continued beyond $x = 3$?
3. How do you determine whether to use parentheses or brackets in interval notation?
4. Can a function's domain and range ever be infinite?
5. What is the significance of a function having endpoints on a graph?

Tip: Always check the endpoints on a graph to determine if they are included in the domain and range by observing whether they are solid dots (included) or open circles (excluded).