Continuity of Functions Is It Discontinued? True Or False

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1.	Identify the picture(s) in which we can see what f is doing for all values of x in the window. I. y = 5x ³– 6x² with -0.4 ≤ x ≤ 0.4 II. y = 5x³– 6x² with -0.6 ≤ x ≤ 0.6 -> Both I and II True False
2.	Four different graphs of the function f(x) = 2x² + 1 are shown below. Which picture best illustrates the fact that if x is within 0.06 of 2, then f(x) is within 0.5 of f(2) = 9? -> True False
3.	Which statement is true for the function f shown below? -> If x is within 0.5 of 3 then f(x) is within 0.5 of 1. True False
4.	We have a function f. We want f(x) to be within 0.5 of f(0). For which of the following functions do we have a guarantee that we can restrict x to find what we want? (x must be allowed to move the same distance from 0 in either direction, and x may not just be set equal to 0.) -> II and III True False
5.	If f(x) = 4 – 2x then when \|x – 1\| < 0.5 we have a guarantee that \|f(x) – 2\| < 1. Identify c, ε, and δ as commonly used in the definition of continuity. -> c = 1, ε = 1, δ = 0.5 True False
6.	Let f(x) = 3x + 1. Then f is continuous at 1 with f(1) = 4. Find the largest value of δ for which if x is within δ of 1, then f(x) is within 0.5 of 4. -> 0.16 True False
7.	Let Then f is continuous at 4 with f(4) = 2. Find the largest value of δ for which if x is within δ of 4, then f(x) is within 0.25 of f(4). -> 0.5 True False
8.	In the formal definition of continuity at x = c, -> ε describes how close we want f(x) and f(c), while δ describes how close x and c need to be. True False
9.	If the function f is continuous at c, then -> for every ε > 0 we can find a δ > 0 such that if \|x – c\| < δ then \|f(x) – f(c)\| < ε. True False
10.	Let , c = 0, and ε = 0.1. Which is the largest value of δ such that if \|x – c\| < δ, then \|f(x) – f(c)\| < ε ? -> True False

Continuity of Functions True or False

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