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The image shows a math problem that asks to calculate the average rate of change for the function \( g(x) = 4x^2 - 5x + 1 \) over different intervals. There are six given intervals:

1. \( 2 \leq x \leq 4 \)
2. \( 2 \leq x \leq 3 \)
3. \( 2 \leq x \leq 2.5 \)
4. \( 2 \leq x \leq 2.25 \)
5. \( 2 \leq x \leq 2.1 \)
6. \( 2 \leq x \leq 2.01 \)

### The average rate of change formula:
The average rate of change of a function \( g(x) \) over an interval \( [a, b] \) is given by:
\[
\text{Average rate of change} = \frac{g(b) - g(a)}{b - a}
\]
We will calculate this for each interval provided.

Would you like me to go through these calculations one by one?

Calculate the average rate of change for the function g(x) = 4x^2 - 5x + 1 over each interval: a) 2 ≤ x ≤ 4, b) 2 ≤ x ≤ 3, c) 2 ≤ x ≤ 2.5, d) 2 ≤ x ≤ 2.25, e) 2 ≤ x ≤ 2.1, f) 2 ≤ x ≤ 2.01.

Learn how to calculate the average rate of change for the quadratic function g(x) = 4x^2 - 5x + 1 over different intervals. This problem is designed for high school students and covers core algebraic concepts.

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