Consider the piecewise defined function x² + 2x – 1 if x < 0 f(x) = if æ > 0 ° Which of the following statements is correct about the function f? The function f is not continuous at x = 0 because the left limit lim f(x) and right limit lim f(x) exist but are different from each other. The function f is continuous at = 0 because the left limit lim ƒ(x) and right limit lim f(x) exist and are the same, but the left and right limits do not equal f(-1). The function f is not continuous at x = 0 because the left limit lim ƒ(x) and right limit lim f(æ) exist and are equal to each other, but ƒ(0) is not defined. The function f is continuous at = 0 because the left limit lim f(x) and right limit lim f(x) exist and are the same and are equal to f(0). None of the above оо
Consider the piecewise defined function x² + 2x – 1 if x < 0 f(x) = if æ > 0 ° Which of the following statements is correct about the function f? The function f is not continuous at x = 0 because the left limit lim f(x) and right limit lim f(x) exist but are different from each other. The function f is continuous at = 0 because the left limit lim ƒ(x) and right limit lim f(x) exist and are the same, but the left and right limits do not equal f(-1). The function f is not continuous at x = 0 because the left limit lim ƒ(x) and right limit lim f(æ) exist and are equal to each other, but ƒ(0) is not defined. The function f is continuous at = 0 because the left limit lim f(x) and right limit lim f(x) exist and are the same and are equal to f(0). None of the above оо
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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Transcribed Image Text:Consider the piecewise defined function
x2 + 2x – 1
if x < 0
-
f (x) =
х — 1
if x > 0`
Which of the following statements is correct about the function f?
O The function f is not continuous at x
O because the left limit lim f(x) and right limit lim f(x) exist but are different from each other.
x→0+
x→0-
O The function f is continuous at x = 0 because the left limit lim f(x) and right limit lim f(x) exist and are the same, but the left and right limits do not equal
x→0-
x→0+
f(-1).
O The function f is not continuous at x =
O because the left limit lim f(x) and right limit lim f(x) exist and are equal to each other, but f(0) is not defined.
x→0-
x→0+
O The function f is continuous at x =
O because the left limit lim f(x) and right limit lim f(x) exist and are the same and are equal to f (0).
x→0-
x→0+
O None of the above
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