Consider the function defined by f(x) = -(x + 1)² +5 if x < 0 x +4 if 0 ≤ x ≤4 1/(x − 3) if x > 4 Graph the function. Is the function continuous at x = 0 and x = 4? Justify your answer by addressing all the conditions for continuity.

College Algebra (MindTap Course List)
12th Edition
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Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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Consider the function defined by
f(x) =
-(x + 1)² +5 if x < 0
x +4
if 0 ≤ x ≤ 4
1/(x-3)
if x > 4
Graph the function. Is the function continuous at x = 0 and x = 4? Justify your answer
by addressing all the conditions for continuity.
Transcribed Image Text:Consider the function defined by f(x) = -(x + 1)² +5 if x < 0 x +4 if 0 ≤ x ≤ 4 1/(x-3) if x > 4 Graph the function. Is the function continuous at x = 0 and x = 4? Justify your answer by addressing all the conditions for continuity.
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