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Determine the x-values where the following functions are not continuous. Label each discontinuity as infinite, removable, or jump. f(x)=(-5)/(x+2)

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Final answer:

The function f(x) = -5/(x+2) is not continuous at x = -2, which is classified as an infinite discontinuity because the function approaches infinity as x approaches -2.

Step-by-step explanation:

To determine the x-values where the function f(x) = -5/(x+2) is not continuous, we need to examine the function and identify any values of x that would cause a disruption in the continuity of f(x). A function is not continuous at points where it is undefined or has an infinite limit. Here, since the denominator x+2 cannot be zero, the function is undefined at x = -2, which creates a discontinuity.

At x = -2, the function has an infinite discontinuity because as x approaches -2, f(x) increases or decreases without bound similar to an asymptote. This is due to f(x) approaching infinity, as mentioned in the reference material regarding the function y = 1/x and its behavior near zero.

Therefore, the function f(x) = -5/(x+2) is not continuous at x = -2, and this is classified as an infinite discontinuity.

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