Find All Points Where the Function Is Discontinuous $\lim f ( x )$

question 11

True/False

Find all points where the function is discontinuous.
-Does $\lim f ( x )$ exist?
$$f ( x ) = \left\{ \begin{array} { l l } - x ^ { 2 } + 1 , & - 1 \leq x < 0 \\2 x , & 0 < x < 1 \\- 4 , & x = 1 \\- 2 x + 4 & 1 < x < 3 \\5 , & 3 < x < 5\end{array} \right.$$

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Definitions:

Perceptual Invariance

The ability of the perceptual system to recognize objects across varying conditions despite changes in angle, distance, or lighting.

Adjusting Differences

The process of accounting for variables that may impact the outcome of a study or analysis, in order to isolate the effect of the independent variable.

False Alarm

An instance in which a warning signal indicates a threat or problem that does not actually exist.

Signal-Detection Theory

A framework describing how stimuli are detected under different conditions, emphasizing the role of decision-making amidst noise.