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.continuousnot 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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Answered: The graph of a function f is given.…

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter3: Linear And Nonlinear Functions

Section3.1: Graphing Linear Functions

Problem 5CYU

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Question

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