Challenge Problem Removing a Discontinuity In Example 5

we graphed the rational function R ( x ) = 2 x 2 − 5 x + 2 x 2 − 4

and found that the graph has a hole at the point ( 2 , 3 4 ) . Therefore, the graph of R is discontinuous at ( 2 , 3 4 ) . We can remove this discontinuity by defining the rational function R using the following piecewise-defined function:

R ( x ) = { 2 x 2 − 5 x + 2 x 2 − 4     if  x ≠ 2   3 4                                                 if  x = 2

Redefine R from Problem 33 so that the discontinuity at x   =   3 is removed.

Redefine R from Problem 33 so that the discontinuity at x   =   3 2 is removed.

R ( x )   =   x 2 + x − 12 x 2 − x − 6