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PLEASEEE HELP !!!
Review the graph of a piecewise function.

On a coordinate plane, a curve goes through closed circle (negative 3, negative 1) and curves up and approaches x = negative 1 in quadrant 1. A line starts at closed circle (negative 1, negative 3) and goes to open circle (1, negative 1). It then goes to open circle (3, negative 1). A horizontal line starts at open circle (3, negative 3) and goes to (5, negative 3). A closed circle is at (3, negative 4).

For which value of x is the function continuous?

PLEASEEE HELP Review the graph of a piecewise function On a coordinate plane a curve goes through closed circle negative 3 negative 1 and curves up and approach class=

Respuesta :

Using the continuity concept, it is found that the function is continuous at x = -3.

What is the continuity concept?

A function f(x) is continuous at x = a if it is defined at x = a, and:

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

In this problem, the function is continuous at x = -3, as:

  • f(3) = -1.
  • [tex]\lim_{x \rightarrow -3^-} f(x) = -1[/tex].
  • [tex]\lim_{x \rightarrow -3^+} f(x) = -1[/tex].

At x = -1, we have that [tex]\lim_{x \rightarrow -1^-} f(x) = \infty[/tex], hence it is not continuous.

The function is not defined for x = 1, and at x = 3, the lateral limits are different.

More can be learned about continuity at https://brainly.com/question/24637240

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