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shown below. • Determine the open intervals on which f (x) is continuous. • Determine, for the values x = -3, , x = 1, and x = 2, for which values ƒ (x) is: o Continuous; o Left-continuous; o Right-continuous. • For each value that f (x) has a discontinuity, state: o Which type of discontinuity it is; o Which of the three criteria for continuity are and are not met; o Why the limit criterion specifically is or is not met. • Determine whether f (x) has one or more horizontal asymptotes, using limits at co and -oo in your explanation.

shown below. • Determine the open intervals on which f (x) is continuous. • Determine, for the values x = -3, , x = 1, and x = 2, for which values ƒ (x) is: o Continuous; o Left-continuous; o Right-continuous. • For each value that f (x) has a discontinuity, state: o Which type of discontinuity it is; o Which of the three criteria for continuity are and are not met; o Why the limit criterion specifically is or is not met. • Determine whether f (x) has one or more horizontal asymptotes, using limits at co and -oo in your explanation.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
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 graphed piecewise function f (x) shown below. • Determine the open intervals on which f (x) is continuous. Determine, for the values x = and x = 2, for which values f (x) is: o Continuous; o Left-continuous; o Right-continuous. • For each value that f (x) has a discontinuity, -3,,x = 1, state: o Which type of discontinuity it is; o Which of the three criteria for continuity are and are not met; • Why the limit criterion specifically is or is not met. Determine whether f (x) has one or more horizontal asymptotes, using limits at o and -o in your explanation. -8 -6- -2
Transcribed Image Text:Consider the graphed piecewise function f (x) shown below. • Determine the open intervals on which f (x) is continuous. Determine, for the values x = and x = 2, for which values f (x) is: o Continuous; o Left-continuous; o Right-continuous. • For each value that f (x) has a discontinuity, -3,,x = 1, state: o Which type of discontinuity it is; o Which of the three criteria for continuity are and are not met; • Why the limit criterion specifically is or is not met. Determine whether f (x) has one or more horizontal asymptotes, using limits at o and -o in your explanation. -8 -6- -2
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