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Describe the continuity of the graphed function. Select all that apply.
The function is continuous at x = -4.
The function has a removable discontinuity at x = -4.
The function has a jump discontinuity at x = -1.
The function has an infinite discontinuity at x = -1.

Describe the continuity of the graphed function Select all that apply The function is continuous at x 4 The function has a removable discontinuity at x 4 The fu class=

Respuesta :

Using continuity concepts, it is found that the correct options are:

  • The function is continuous at x = -4.
  • The function has an infinite discontinuity at x = -1.

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A function f(x) is continuous at x = a if:

[tex]\lim_{x \rightarrow a^{-}} f(x) = \lim_{x \rightarrow a^{+}} f(x) = f(a)[/tex]

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  • At x = -4, there are no changes in the definition of the function, thus, it is continuous.
  • At x = -1, we have that:

[tex]\lim_{x \rightarrow -1^-} f(x) = 0[/tex]

[tex]\lim_{x \rightarrow -1^+} f(x) = f(1) = 1[/tex]

  • A different definition depending on the which side of -1 the function is, thus, it is a jump discontinuity.

A similar problem is given at https://brainly.com/question/21447009

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