To answer the question about the domain and range of the function $f$ based on its graph, I'll guide you through the steps:

Domain:

The domain of a function represents all the possible $x$-values for which the function is defined. From the graph of $f$, observe the $x$-values for which the graph exists.

• Identify the leftmost point (smallest $x$-value) and the rightmost point (largest $x$-value) on the graph.

Range:

The range of a function represents all the possible $y$-values that the function can take. From the graph of $f$, observe the $y$-values covered by the graph.

• Identify the lowest point (smallest $y$-value) and the highest point (largest $y$-value) on the graph.

Interval Notation:

Once you've identified the domain and range, you express them using interval notation.

• Domain in Interval Notation: $[a, b]$ where $a$ is the smallest $x$-value and $b$ is the largest $x$-value.
• Range in Interval Notation: $[c, d]$ where $c$ is the smallest $y$-value and $d$ is the largest $y$-value.

Example Explanation:

If the graph starts at $x = -2$ and ends at $x = 5$, the domain is $[-2, 5]$. If the graph covers $y$-values from $y = 1$ to $y = 4$, the range is $[1, 4]$.

Please describe or upload the graph so I can give a more accurate answer!

Do you want details or have any questions?
Here are 5 related questions to think about:

1. How do we handle open or closed intervals in domain and range?
2. What does it mean if the graph has breaks or gaps?
3. How would the domain change if the function included vertical asymptotes?
4. How does the graph's behavior at the endpoints affect the range?
5. What happens to the range if the graph is reflected across the x-axis?

Tip: Always double-check if the graph includes points at the endpoints or if they are open, as this affects whether the interval is open or closed.