f(x) = { if

A.

Because as concerns positive numbers greater than 4, you can use the 1+x part of the function to find the limit without having to graph it

B. This is a piecewise function. Based on the conditions of the function, a piecewise function can be continuous or discontinuous depending on whether the stipulations given cause there to be a discontinuity. In the case of this piecewise function, it IS continuous on the interval (0,10) because there is no break in the graph. The two pieces of this function intersect at x=4. Should the function have read as:

f(x) = { if

Then the function would not be continuous, because x = 2 would not be included in the domain of the function. There would be a hole at x=2