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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?

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 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]

These three values are equal for x = -3, hence the function is continuous at x = -3.

For the other options, the function is not continuous for the reasons given as follows:

  • x = -1: Different lateral limits.
  • x = 1: f(1) is not defined.
  • x = 3: Different lateral limits.

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

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