Let's break down the graph and questions provided in your image step by step.

(a) Domain and Range:

• Domain: The domain represents all possible $x$-values for which the function $f(x)$ is defined. From the graph, we can observe that the function starts at $x = -4$ and continues to $x = 4$.

  • Domain: $[-4, 4]$

• Range: The range is the set of all possible $y$-values that the function can take. From the graph, we can see that the lowest point on the $y$-axis is $-2$, and the highest point is $3$.

  • Range: $[-2, 3]$

(b) Find $f(0)$ and $f(2)$:

• $f(0)$: From the graph, when $x = 0$, the corresponding $y$-value is $1$. Thus, $f(0) = 1$.
• $f(2)$: From the graph, when $x = 2$, the corresponding $y$-value is $3$. Thus, $f(2) = 3$.

(c) Find the value(s) of $x$ such that $f(x) = 2$:

• To find $x$ when $f(x) = 2$, we locate $y = 2$ on the graph. The corresponding $x$-value for this point is $x = 1$.
  • So, $x = 1$.

(d) Determine the intervals on which $f(x)$ is increasing and decreasing:

• Increasing: A function is increasing when the graph rises as we move from left to right. From the graph:

  • The function increases from $x = 0$ to $x = 4$.
  • So, $f(x)$ is increasing on $(0, 4]$.

• Decreasing: A function is decreasing when the graph falls as we move from left to right. From the graph:

  • The function decreases from $x = -4$ to $x = 0$.
  • So, $f(x)$ is decreasing on $[-4, 0]$.

Would you like more details on any of these answers?

Here are five related questions to further your understanding:

1. What is the difference between the domain and the range of a function?
2. How can you determine the increasing and decreasing intervals of a function without a graph?
3. How would the range change if the function were stretched vertically?
4. How do you find $f(x)$ for non-integer values of $x$ from the graph?
5. Can a function have more than one interval where it is increasing or decreasing?

Tip: Always check the behavior of the function at critical points like where it changes from increasing to decreasing or vice versa.