Concept explainers
To Prove: The constant rate of change theorem.
Given information: The constant rate of change theorem states that a function defined on all real numbers is a linear function if and only if it has nonzero average rate of change between any two points on the graph.
Formula used: The slope
Proof:
The average rate of change of linear function is constant:
The ratio of output to input stays the same at any given point on the function. This constant rate of change is the slope.
For instance, if the linear function is
Hence, the average rate of change remain the same for the entire domain of the linear function.
Chapter 2 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning