For which type of function does the average rate of change produce the same value for any interval of the domain on the function? Why does this occur for this type of function?

Question

For which type of function does the average rate of change produce the same value for any interval of the domain on the function? Why does this occur for this type of function?
*Hint* you have 3 choices: Linear, Quadratic and Exponential

very simple explanation

GPT-4o mini · Answer

The type of function for which the average rate of change produces the same value for any interval of the domain is a linear function.

Explanation:

A linear function can be written in the form \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. The average rate of change between any two points on a linear function is always equal to the slope \( m \). Since the slope is constant, the average rate of change does not vary regardless of the interval you choose on the function.

In contrast, quadratic and exponential functions have changing slopes, which means their average rates of change vary depending on the interval chosen.