Let's break down the problem step by step.

(a) Finding the Domain and Range of $g$:

• Domain: The domain of a function refers to all the possible values of $x$ for which the function is defined. If the graph of $g(x)$ extends infinitely in both directions along the x-axis without any breaks or vertical asymptotes, then the domain is $(-\infty, \infty)$, meaning all real numbers.

• Range: The range of a function is the set of all possible output values (or $y$-values) from the function. If the graph extends vertically across all $y$-values from negative infinity to positive infinity, the range is $(-\infty, \infty)$.

(b) Using the Formula to Evaluate $g(-1)$ and $g(1)$:

Without the specific formula provided for $g(x)$, I will assume you are referring to values you obtained from the graph or a formula you've used. Based on the information given:

• $g(-1) = -2$ is already provided, so we know that for $x = -1$, the value of $g(x)$ is $-2$.

We will also need to compute $g(1)$ using the same approach, assuming there is either a formula or graphical data available.

(c) Using the Graph of $g$ to Evaluate $g(-1)$ and $g(1)$:

• If we are using the graph to evaluate $g(-1)$, we locate $x = -1$ on the x-axis and then find the corresponding point on the graph. According to the problem, $g(-1) = -2$.

• Similarly, for $g(1)$, we locate $x = 1$ on the graph and check the corresponding $y$-value.

Summary:

• Domain: $(-\infty, \infty)$ (assuming the graph extends without any breaks or restrictions).
• Range: $(-\infty, \infty)$ (assuming the graph covers all y-values).
• $g(-1)$ from the formula: $-2$.
• $g(1)$ would need to be determined from either the graph or the formula.

Would you like to provide more information on the graph or the formula, or do you need further clarification?

Relative Questions:

1. How do you determine the domain of a function from a graph?
2. What is the significance of the range in understanding a function?
3. How can we use the graph to evaluate the value of a function at specific points?
4. What types of functions have a domain of $(-\infty, \infty)$?
5. How do asymptotes affect the domain and range of a function?

Tip:

Always check for any holes, vertical asymptotes, or breaks in the graph to correctly determine the domain and range of a function.