Question

Consider function g. What is the average rate of change of function g over the interval (-4, 3)? A. 1/2 B. -1/7 C. 2 D. 1/1

Answer 1

The average rate of change of function g over the interval (-4, 3) is
`\(\text{B. } -(1)/(7)\).` Thus the correct option is B.

Step-by-step explanation:

The average rate of change of a function over an interval a, b is given by the formula:

`\[ \text{Average Rate of Change} = (f(b) - f(a))/(b - a) \]`

In this case, the interval is (-4, 3), and the function is denoted as g. Therefore, the average rate of change of g over the interval (-4, 3) can be expressed as:

`\[ \text{Average Rate of Change} = (g(3) - g(-4))/(3 - (-4)) \]`

By evaluating
`\(g(3)\)` and
`\(g(-4)\)` based on the given function, and simplifying the expression, we find that the average rate of change is
`\(\text{B. } -(1)/(7)\).`

This result indicates that, on average, the function \(g\) decreases by
`\((1)/(7)\)` units for each unit increase in the independent variable over the specified interval. The negative sign indicates a decreasing trend, while the fraction
`\((1)/(7)\)` quantifies the average rate of change.

The complete question is:

Consider the function g(x). What is the average rate of change of function g over the interval (-4, 3)?

A.
`\( (1)/(2) \)`

B.
`\( -(1)/(7) \)`

C.
`\( 2 \)`

D.
`\( (1)/(1) \)`