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Consider a dataset of numbers Y1, Y2, ..., Yn. Prove or find a counterexample to disprove each of the following statements. Consider the linear function f(x) = 9x — 4. a) If ab, show that ƒ(a) ≤ ƒ(b). b) c) Both of the statements below are true, but only one is a consequence of the property you proved in part (a). Which is it? Show that this statement is true, using the result of part (a). 1. Mean(f(x1), ,..., f(xn)) = f(Mean(x1,...,xn)) 2. Median (f(x1), . . ., f(xn)) = f(Median(x1,...,xn)) Now, prove the other statement. Note your proof should not depend on the property you proved in part (a).

Consider a dataset of numbers Y1, Y2, ..., Yn. Prove or find a counterexample to disprove each of the following statements. Consider the linear function f(x) = 9x — 4. a) If ab, show that ƒ(a) ≤ ƒ(b). b) c) Both of the statements below are true, but only one is a consequence of the property you proved in part (a). Which is it? Show that this statement is true, using the result of part (a). 1. Mean(f(x1), ,..., f(xn)) = f(Mean(x1,...,xn)) 2. Median (f(x1), . . ., f(xn)) = f(Median(x1,...,xn)) Now, prove the other statement. Note your proof should not depend on the property you proved in part (a).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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part c

Consider a dataset of numbers Y1, Y2, ..., Yn. Prove or find a counterexample to disprove each of the following statements. Consider the linear function f(x) = 9x — 4. a) If ab, show that ƒ(a) ≤ ƒ(b). b) c) Both of the statements below are true, but only one is a consequence of the property you proved in part (a). Which is it? Show that this statement is true, using the result of part (a). 1. Mean(f(x1), ,..., f(xn)) = f(Mean(x1,...,xn)) 2. Median (f(x1), . . ., f(xn)) = f(Median(x1,...,xn)) Now, prove the other statement. Note your proof should not depend on the property you proved in part (a).
Transcribed Image Text:Consider a dataset of numbers Y1, Y2, ..., Yn. Prove or find a counterexample to disprove each of the following statements. Consider the linear function f(x) = 9x — 4. a) If ab, show that ƒ(a) ≤ ƒ(b). b) c) Both of the statements below are true, but only one is a consequence of the property you proved in part (a). Which is it? Show that this statement is true, using the result of part (a). 1. Mean(f(x1), ,..., f(xn)) = f(Mean(x1,...,xn)) 2. Median (f(x1), . . ., f(xn)) = f(Median(x1,...,xn)) Now, prove the other statement. Note your proof should not depend on the property you proved in part (a).
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