Describe the interval(s) on which the function is continuous. f(x)={ (x^2-1)/(x-1), x ≠

step 1 We're given a piecewise function given by x squared minus 1 over x minus 1 and 2. Now, we're ask

Describe the interval(s) on which the function is...

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Key Concepts

Function Continuity

Function continuity is the property of a function where, at a given point, the limit of the function as it approaches that point equals the function's value at that point. This means there are no sudden jumps, gaps, or holes at that point, which is crucial in determining the intervals over which the function behaves predictably.

Removable Discontinuity

A removable discontinuity occurs when a function is not defined or is defined differently at a particular point even though the limit exists. This often happens when an algebraic expression can be simplified by canceling a common factor, suggesting that redefining the function at the problematic point could restore continuity.

Piecewise Functions

Piecewise functions are defined by different expressions in different parts of their domain. Continuity analysis for such functions involves checking not only the continuity within each portion of the domain but also ensuring that the different pieces meet in a way that preserves continuity at the boundary points.

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