The problem asks to find the average rate of change of the function $g(x) = \frac{-15}{x} + 19$ over the interval $[-13, -10]$.

The average rate of change formula is:

$\text{Average Rate of Change} = \frac{g(b) - g(a)}{b - a}$ where $a = -13$ and $b = -10$.

Step 1: Calculate $g(a)$

Substitute $a = -13$ into the function: $g(-13) = \frac{-15}{-13} + 19 = \frac{15}{13} + 19$ $g(-13) = \frac{15}{13} + \frac{247}{13} = \frac{262}{13}$ So, $g(-13) = \frac{262}{13} \approx 20.15$.

Step 2: Calculate $g(b)$

Substitute $b = -10$ into the function: $g(-10) = \frac{-15}{-10} + 19 = \frac{15}{10} + 19$ $g(-10) = 1.5 + 19 = 20.5$

Step 3: Apply the Average Rate of Change Formula

$\text{Average Rate of Change} = \frac{g(-10) - g(-13)}{-10 - (-13)} = \frac{20.5 - 20.15}{-10 + 13}$ $= \frac{0.35}{3} \approx 0.117$

Thus, the average rate of change is approximately $0.1$ (rounded to the nearest tenth).

Would you like further details or clarifications?

Here are some related questions:

1. How is the average rate of change similar to the slope of a line?
2. Can the average rate of change ever be negative?
3. What would the rate of change be for a constant function?
4. How does the interval choice affect the average rate of change?
5. What is the geometric meaning of the average rate of change?

Tip: Always double-check the interval endpoints when applying the formula for average rate of change.