Let's analyze the graph to answer the questions one by one:

(a) Domain of $f$:

The domain refers to all the possible values of $x$ for which the function is defined.

• From the graph, $f(x)$ starts at $x = -6$ and ends at $x = 6$.

  Domain: $[-6, 6]$

(b) Range of $f$:

The range refers to all the possible values of $f(x)$.

• The lowest point on the graph is at $y = -6$ and the highest point is at $y = 4$.

  Range: $[-6, 4]$

(c) Zeros of $f$:

Zeros are the values of $x$ where $f(x) = 0$.

• The graph intersects the $x$-axis at $x = -4$, $x = 2$, and $x = 6$.

  Zeros: $x = -4, 2, 6$

(d) $f(3.5)$:

To find $f(3.5)$, locate $x = 3.5$ on the graph and observe the corresponding $y$-value.

• At $x = 3.5$, $f(x) = 3$.

  $f(3.5) = 3$

(e) Intervals on which $f$ is increasing:

A function is increasing where the graph moves upwards as $x$ increases.

• From $x = -6$ to $x = 2$, the graph is increasing.

  Increasing on: $(-6, 2)$

(f) Intervals on which $f$ is decreasing:

A function is decreasing where the graph moves downwards as $x$ increases.

• From $x = 2$ to $x = 6$, the graph is decreasing.

  Decreasing on: $(2, 6)$

(g) Values for which $f(x) \leq 0$:

These are the values of $x$ where the graph lies below or on the $x$-axis.

• The graph is at or below the $x$-axis for $x \in [-6, -4] \cup [2, 6]$.

  Values where $f(x) \leq 0$: $x \in [-6, -4] \cup [2, 6]$

(h) Any relative maxima or minima:

• Relative Maximum: The highest point in a region, occurs at $x = 2$ with $f(2) = 4$.

• Relative Minimum: The lowest point in a region, occurs at $x = -6$ and $x = 6$ with $f(-6) = f(6) = -6$.

  Relative Max: $(2, 4)$
  Relative Min: $(-6, -6)$ and $(6, -6)$

(i) Value(s) of $x$ for which $f(x) = 3$:

Find the points where the graph intersects the line $y = 3$.

• $f(x) = 3$ at $x = 3.5$ and $x = 0$.

  $f(x) = 3$ at $x = 0$ and $x = 3.5$

(j) Is $f(2)$ positive or negative?

• From the graph, at $x = 2$, $f(2) = 4$, which is positive.

  $f(2)$ is positive.

Let me know if you need further details on any of these answers. Here are some related questions to expand your understanding:

1. What is the significance of the domain and range in graph analysis?
2. How can we determine if a function is increasing or decreasing using its derivative?
3. What are the implications of having multiple zeros in a function?
4. How can the concept of relative maxima and minima be used in real-world problems?
5. How would you algebraically determine the zeros of a function from its equation?

Tip: Understanding the shape and behavior of the graph can help in identifying intervals of increase and decrease. Always look for key points like turning points and intersections with the axes.