The image you uploaded contains a graph of a function $y = f(x)$ along with several questions related to that graph. I'll help you analyze and solve the problems one by one based on the visual information provided.

Questions:

(a) Determine $f(-3)$:

• To find $f(-3)$, locate $x = -3$ on the x-axis and observe the y-coordinate of the point on the graph.
• From the graph, at $x = -3$, $f(x)$ appears to be at $y = 0$.
• Thus, $f(-3) = 0$.

(b) Find all values for which $f(x) = 1$:

• To find where $f(x) = 1$, observe where the graph intersects the line $y = 1$.
• The graph seems to cross $y = 1$ at $x = -4$ and $x = 1$.
• Therefore, $f(x) = 1$ at $x = -4$ and $x = 1$.

(c) Find all x-values for which $f(x) = -1$:

• We need to check where the graph intersects $y = -1$.
• The graph crosses $y = -1$ at $x = -2$ and $x = 3$.
• So, $f(x) = -1$ at $x = -2$ and $x = 3$.

(d) List the x-intercepts in ascending order:

• The x-intercepts are points where the graph crosses the x-axis (i.e., where $f(x) = 0$).
• From the graph, the x-intercepts are $x = -3$, $x = 0$, and $x = 2$.
• In ascending order: $-3, 0, 2$.

(e) Determine the domain of $f$:

• The domain refers to the set of all x-values for which the function is defined.
• From the graph, it appears that the function is defined for all real numbers.
• Therefore, the domain of $f$ is $(-\infty, \infty)$.

(f) Determine the range of $f$:

• The range is the set of all possible y-values the function can take.
• Based on the graph, the lowest point seems to be at $y = -2$ and the highest point is $y = 2$.
• So, the range of $f$ is $[-2, 2]$.

Would you like any further clarifications or details on any of these answers?

Relative Questions:

1. What are the critical points of the function $f(x)$?
2. How would you determine if the function is increasing or decreasing in certain intervals?
3. What is the behavior of $f(x)$ as $x$ approaches infinity or negative infinity?
4. Can you determine the local maximum and minimum points of the graph?
5. How would you write the intervals of concavity for the graph?

Tip:

Always analyze the graph's x-intercepts, y-intercepts, and turning points when determining important characteristics of a function such as its domain, range, and intercepts.