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52. PROVE: Functions with Constant Rate of Change Are Linear Suppose that the function f has the same average rate of change e between any two points. (a) Find the average rate of change of ƒ between the points a and x to show that f(x) – f(a) х — а (b) Rearrange the equation in part (a) to show that f(x) = cx + (f(a) – ca) How does this show that f is a linear function? What is the slope, and what is the y-intercept?

52. PROVE: Functions with Constant Rate of Change Are Linear Suppose that the function f has the same average rate of change e between any two points. (a) Find the average rate of change of ƒ between the points a and x to show that f(x) – f(a) х — а (b) Rearrange the equation in part (a) to show that f(x) = cx + (f(a) – ca) How does this show that f is a linear function? What is the slope, and what is the y-intercept?

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter8: Graphing Quadratic Functions
Section: Chapter Questions
Problem 17CT
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Prove: Functions with Constant Rate of Change Are Linear

52. PROVE: Functions with Constant Rate of Change Are Linear Suppose that the function f has the same average rate of change e between any two points. (a) Find the average rate of change of ƒ between the points a and x to show that f(x) – f(a) х — а (b) Rearrange the equation in part (a) to show that f(x) = cx + (f(a) – ca) How does this show that f is a linear function? What is the slope, and what is the y-intercept?
Transcribed Image Text:52. PROVE: Functions with Constant Rate of Change Are Linear Suppose that the function f has the same average rate of change e between any two points. (a) Find the average rate of change of ƒ between the points a and x to show that f(x) – f(a) х — а (b) Rearrange the equation in part (a) to show that f(x) = cx + (f(a) – ca) How does this show that f is a linear function? What is the slope, and what is the y-intercept?
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