The image shows a graph of a function $g(x)$ with some evaluations and the domain and range to be determined.

Part (a): Evaluations of the function

We can find the values of $g(x)$ at specific points by reading them from the graph:

• $g(-4) = 1$ (the point $(-4, 1)$ is on the graph)
• $g(-2) = 3$ (the point $(-2, 3)$ is on the graph)
• $g(0) = -2$ (the point $(0, -2)$ is on the graph)
• $g(2) = 1$ (the point $(2, 1)$ is on the graph)
• $g(4) = -1$ (the point $(4, -1)$ is on the graph)

Part (b): Domain and Range

• Domain: The domain is the set of all $x$-values for which the function is defined. The graph extends from $x = -4$ to $x = 4$, so the domain is $[-4, 4]$.

• Range: The range is the set of all possible $y$-values that the function takes. From the graph, the lowest $y$-value is $-2$, and the highest $y$-value is $3$, so the range is $[-2, 3]$.

Summary:

• Evaluations:

  • $g(-4) = 1$
  • $g(-2) = 3$
  • $g(0) = -2$
  • $g(2) = 1$
  • $g(4) = -1$

• Domain: $[-4, 4]$

• Range: $[-2, 3]$

Would you like more details or have any questions?

Here are five related questions to further your understanding:

1. How can you determine if the function is continuous from the graph?
2. What is the difference between the domain and range of a function?
3. Could you determine if the function has any symmetry (e.g., even or odd)?
4. How would the domain and range change if the graph extended beyond $x = 4$?
5. How do you find the maximum and minimum values of a function from its graph?

Tip: When analyzing graphs, always note the highest and lowest points to determine the range, and check the farthest points along the x-axis for the domain!