Example Problem 1 - Finding Removable Discontinuities Identify the type of discontinuity in the following function: $$f(x)=\frac{x^2+x-12}{x^2-5x+6} $$ Step 1:Factor the polynomials in the numerator and denominator of the given function as much as possible. ...
Using the graph shown below, identify and classify each point of discontinuity. Step 1 The table below lists the location (x-value) of each discontinuity, and the type of discontinuity. xType−7Mixed−3Removable2Jump4Infinite6Endpoint ...
A hole in a rational function is a removable discontinuity that breaks continuity for that function. Finding a hole within a rational function helps identify specific x-values that are to be excluded in intervals when using certain theorems (i.e. Mean Value Theorem, Integrals, Rolle’s Theorem...
Identify the Point: Determine the point(s) where the function needs modification. This could be where the function is undefined or discontinuous. Evaluate the Limit: If the function is approaching a specific value near this point, that value is often used for redefinition. Redefine the Function...
Identify an asymptotic discontinuity. These discontinuous functions have an asymptote that causes the parts of the function to tend toward an x value without reaching it. 4 Trace the curve left to right. As a general rule, a function is discontinuous if you need to pick up your pencil as ...