The graph of a function f is given. The x y-coordinate plane is given. A curve with 3 parts is graphed. The first part is linear, enters the window in the second quadrant, goes down and right, crosses the x-axis at approximately x = −0.33, crosses the y-axis at y = −0.25, and ends at the open point (1, −1). The second part is the point (1, 1). The third part is linear, begins at the open point (1, −1), goes up and right, crosses the x-axis at x = 2, and exits the window in the first quadrant. Determine whether f is continuous on its domain. continuous not continuous If it is not continuous on its domain, say why. lim x→1+ f(x) ≠ lim x→1− f(x), so lim x→1 f(x) does not exist. The function is not defined at x = 1. The graph is continuous on its domain. lim x→1 f(x) = −1 ≠ f(1)
The graph of a function f is given. The x y-coordinate plane is given. A curve with 3 parts is graphed. The first part is linear, enters the window in the second quadrant, goes down and right, crosses the x-axis at approximately x = −0.33, crosses the y-axis at y = −0.25, and ends at the open point (1, −1). The second part is the point (1, 1). The third part is linear, begins at the open point (1, −1), goes up and right, crosses the x-axis at x = 2, and exits the window in the first quadrant. Determine whether f is continuous on its domain. continuous not continuous If it is not continuous on its domain, say why. lim x→1+ f(x) ≠ lim x→1− f(x), so lim x→1 f(x) does not exist. The function is not defined at x = 1. The graph is continuous on its domain. lim x→1 f(x) = −1 ≠ f(1)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The graph of a function f is given.
The x y-coordinate plane is given. A curve with 3 parts is graphed.
- The first part is linear, enters the window in the second quadrant, goes down and right, crosses the x-axis at approximately x = −0.33, crosses the y-axis at y = −0.25, and ends at the open point (1, −1).
- The second part is the point (1, 1).
- The third part is linear, begins at the open point (1, −1), goes up and right, crosses the x-axis at x = 2, and exits the window in the first quadrant.
Determine whether f is continuous on its domain.
continuous
not continuous
If it is not continuous on its domain, say why.
lim
x→1+
f(x) ≠
lim
x→1−
f(x), so
lim
x→1
f(x) does not exist.
The function is not defined at x = 1.
The graph is continuous on its domain.
lim
x→1
f(x) = −1 ≠ f(1)
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