In Problems 83-98, find the difference quotient of f; that is, find (f(x+h)-f(x))/(h), h ≠0, for

step 1 Here we're going to find F of X plus H minus F of X over H such that H does not equal zero for t

In Problems 83-98, find the difference quotient of f; that...

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Key Concepts

Difference Quotient

The difference quotient is a formula used to compute the average rate of change of a function over a small interval. It is defined as (f(x + h) - f(x)) / h, where h is a non-zero increment. This concept is fundamental in calculus because it leads to the definition of the derivative as h approaches zero.

Linear Function

A linear function is a function that creates a straight line graph, typically expressed in the form f(x) = mx + b, where m represents the slope and b represents the y-intercept. For linear functions, the difference quotient simplifies directly to the constant slope, demonstrating that the average rate of change is the same at every point.

Algebraic Simplification

Algebraic simplification involves reducing expressions to their simplest form through operations such as combining like terms and canceling common factors. When applied to the difference quotient, it ensures that the expression is concise and reveals important properties such as the slope in the case of linear functions.

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