AP Calculus BC LIM-2.C—Determine values of x or solve for parameters that make discontinuous functions continuous, if possible Concept

LIM-2.C Determine values of x or solve for parameters that make discontinuous functions continuous, if possible.
LIM-2.C.1 If the limit of a function exists at a discontinuity in its graph, then it is possible to remove the discontinuity by defining or redefining the value of the function at that point, so it equals the value of the limit of the function as x approaches that point.
LIM-2.C.2 In order for a piecewise-defined function to be continuous at a boundary to the partition of its domain, the value of the expression defining the function on one side of the boundary must equal the value of the expression defining the other side of the boundary, as well as the value of the function at the boundary.
Enduring understanding LIM-2: Reasoning with definitions, theorems, and properties can be used to justify claims about continuity.