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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.

Find the average rate of change of g(x) = -15/x + 19 over the interval [-13, -10]. Write your answer as an integer, fraction, or decimal rounded to the nearest tenth. Simplify any fractions.

Learn how to calculate the average rate of change for the function g(x) = -15/x + 19 over the interval [-13, -10]. This solution covers important algebraic concepts, including the application of the average rate of change formula.

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