The given function is $f(x) = 4x - 5$ with a domain $x \in [1, 5]$, and we are asked to determine the range of this function.

Step 1: Find the function values at the endpoints of the domain

• For $x = 1$: $f(1) = 4(1) - 5 = 4 - 5 = -1$
• For $x = 5$: $f(5) = 4(5) - 5 = 20 - 5 = 15$

Step 2: The range of a linear function is between the minimum and maximum values of $f(x)$ over the given domain. Since the function is increasing (positive slope), the minimum value is at $x = 1$ and the maximum value is at $x = 5$.

Thus, the range of the function is $[-1, 15]$.

Conclusion:

The correct answer is A. [-1, 15].

Would you like further details or explanations? Here are 5 related questions to explore:

1. How do you find the range of a quadratic function?
2. What is the significance of the slope in determining the behavior of a linear function?
3. How do you solve for the inverse of a linear function?
4. Can the range of a linear function ever be a single point?
5. How would the range change if the domain was different?

Tip: The range of a function is highly dependent on the behavior (increasing or decreasing) and the domain of the function, especially for linear and polynomial functions.