**What is the domain of \[g\]?**

Choose 1 answer:

Choose 1 answer:

(Choice A)   

\[-5 \leq x \leq -3\]

A

\[-5 \leq x \leq -3\]

(Choice B)   

\[-5 \leq x \leq 7\]

B

\[-5 \leq x \leq 7\]

(Choice C)   

\[-7 \leq x \leq 7\]

C

\[-7 \leq x \leq 7\]

(Choice D)   

\[-7 \leq x \leq -3\]

D

\[-7 \leq x \leq -3\]

The domain of a function is the set of all possible \(x\) values (input values) for which the function is defined.

Without a graph or explicit function definition for \(g(x)\), the question likely refers to the \(x\) values over which \(g(x)\) is defined, similar to the previous question. If \(g(x)\) is defined over a range of \(x\) values, these would correspond to the endpoints of the intervals given in the options.

Given the multiple choices:
- **(A)** \([-5 \leq x \leq -3]\)
- **(B)** \([-5 \leq x \leq 7]\)
- **(C)** \([-7 \leq x \leq 7]\)
- **(D)** \([-7 \leq x \leq -3]\)

If the function \(g(x)\) spans from an \(x\) value of \(-7\) to \(7\), then the domain would be \([-7 \leq x \leq 7]\). This matches **Choice C**.

**Correct answer:**
- **(Choice C) \([-7 \leq x \leq 7]\)**

Would you like further explanation, or do you have any questions?

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Here are some follow-up questions to consider:
1. How does the domain of a function relate to its graph?
2. What is the domain of the function \(h(x) = \sqrt{x}\)?
3. How can you determine the domain of a function involving fractions?
4. If a function is only defined for certain integer values, what is its domain?
5. What would the domain be for a function defined as \(k(x) = \frac{1}{x}\)?
6. How does the domain change for a piecewise function?
7. How would the domain change if \(g(x)\) had a vertical asymptote?
8. What does it mean if the domain of a function is all real numbers?

**Tip:** When determining the domain from a graph, look at the horizontal extent of the graph along the \(x\)-axis.

Learn how to determine the domain of a function with an example problem. This page explains the concept of domain in mathematics and provides a step-by-step solution to a typical domain determination question. Suitable for high school students and anyone studying functions and their properties.

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