Let's analyze the graph in the image and address each question.

(a) Domain of f:

The domain is the set of all possible input values (x-values) for the function. Based on the graph, it appears that the function extends indefinitely in both directions along the x-axis. Hence, the domain of $f$ is: $\text{Domain: } (-\infty, \infty)$

(b) Range of f:

The range is the set of all output values (y-values) the function can take. From the graph, the lowest point is at $y = -2$, and the function extends upwards without bound. Thus, the range of $f$ is: $\text{Range: } [-2, \infty)$

(c) X-intercepts:

X-intercepts are the points where the graph crosses the x-axis. From the graph, the x-intercepts are at $x = -3$ and $x = 1$. So the x-intercepts are: $x = -3, x = 1$

(d) Y-intercept:

The y-intercept is the point where the graph crosses the y-axis. This occurs at $y = -1$. Therefore, the y-intercept is: $y = -1$

(e) Intervals on which f is increasing:

The function is increasing when the graph is going upwards as we move from left to right. From the graph, the function increases on the interval $(x = -1, \infty)$. So, the interval is: $(-1, \infty)$

(f) Intervals on which f is decreasing:

The function is decreasing when the graph is going downwards as we move from left to right. From the graph, the function decreases on the interval $(-\infty, -1)$. So, the interval is: $(-\infty, -1)$

(g) Intervals on which f is constant:

There are no intervals where the function is constant (i.e., horizontal). Hence, there are no such intervals.

(h) The number at which f has a relative minimum:

A relative minimum occurs at the lowest point in a particular section of the graph. The graph has a relative minimum at $x = -1$.

(i) The relative minimum of f:

The value of the relative minimum is the y-coordinate at $x = -1$, which is $y = -2$. So, the relative minimum value is: $y = -2$

(j) f(-4):

To find $f(-4)$, we check the y-value of the function when $x = -4$. From the graph, $f(-4) = 0$.

(k) The values of x for which $f(x) = 3$:

To solve $f(x) = 3$, we look for the points on the graph where the y-value is 3. There are no points on the graph where $f(x) = 3$, so there are no such values of $x$.

(l) Is f even, odd, or neither?:

A function is even if it is symmetric with respect to the y-axis, and odd if it is symmetric with respect to the origin. The given function is not symmetric with respect to the y-axis or the origin, so it is neither even nor odd.

Would you like further details or have any questions on this? Here are 5 related questions that could deepen your understanding:

1. How can you tell whether a function is increasing or decreasing just from its graph?
2. Why is the range of the function restricted to values greater than or equal to -2?
3. What is the significance of x- and y-intercepts in the context of a function?
4. How do relative minimum and maximum points help in analyzing functions?
5. How can you determine whether a function is even, odd, or neither from its equation?

Tip: When solving for intercepts, remember that for x-intercepts, set $y = 0$, and for y-intercepts, set $x = 0$.