The problem provides the income tax function $T(g) = 4250 + 0.25(g - 30,700)$, which is defined for a specific range of adjusted gross income $g$.

(a) Domain of the Function $T(g)$:

The domain of a function refers to all possible input values (in this case, the values of $g$) for which the function is defined.

Here, the function $T(g)$ is defined for:

$30,700 \leq g \leq 74,300$

Conclusion:

• Domain: The domain of the function $T(g)$ is the closed interval $[30,700, 74,300]$.

Would you like more details, or do you have any questions?

Here are some related questions:

1. How do you find the range of the function $T(g)$?
2. What is the meaning of the slope in the linear function $T(g)$?
3. How would you find the inverse function $g(T)$ for the given problem?
4. How does the function $T(g)$ change if the tax rate changes?
5. How would the function $T(g)$ change if the starting amount $4250$ was different?

Tip: When interpreting functions, always check the domain and range to ensure the function is correctly applied to the problem context.