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5. Suppose instead we had the following tax structure. 10x, .12x, .22x, f(x) = .24x, x ≤ 9,950 9,950 < x≤ 40,525 40,525 < x≤ 86,375 86,375 < x≤ 164,925 164,925 < x < 209,425 209,425 < x≤ 523,600 x> 523,600 .32x, .35x, 37x, where x is a person's taxable income. Is this function continuous at x = 40,525? Explain.

5. Suppose instead we had the following tax structure. 10x, .12x, .22x, f(x) = .24x, x ≤ 9,950 9,950 < x≤ 40,525 40,525 < x≤ 86,375 86,375 < x≤ 164,925 164,925 < x < 209,425 209,425 < x≤ 523,600 x> 523,600 .32x, .35x, 37x, where x is a person's taxable income. Is this function continuous at x = 40,525? Explain.

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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5. Suppose instead we had the following tax structure. .10x, x ≤ 9,950 .12x, .22x, f(x) = .24x, ,32x, 9,950 < x≤ 40,525 40,525 < x≤ 86,375 86,375 x ≤ 164,925 164,925 < x≤ 209,425 209,425 < x < 523,600 x> 523,600 .35x, .37x. where x is a person's taxable income. Is this function continuous at x = 40,525? Explain. 6. Explain in terms of the real-world situation why this would not be a logical tax structure. That is, using your work from question five (5), explain why continuity is important for the function that tells us income tax due. Consider people who fall at a taxable income near an endpoint of one of the equation's domains.
Transcribed Image Text:5. Suppose instead we had the following tax structure. .10x, x ≤ 9,950 .12x, .22x, f(x) = .24x, ,32x, 9,950 < x≤ 40,525 40,525 < x≤ 86,375 86,375 x ≤ 164,925 164,925 < x≤ 209,425 209,425 < x < 523,600 x> 523,600 .35x, .37x. where x is a person's taxable income. Is this function continuous at x = 40,525? Explain. 6. Explain in terms of the real-world situation why this would not be a logical tax structure. That is, using your work from question five (5), explain why continuity is important for the function that tells us income tax due. Consider people who fall at a taxable income near an endpoint of one of the equation's domains.
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