Suppose that the piecewise function f is defined byf$($x$)=$x$3,$x$13$x$2+2$x$3,$x$>1.$

Determine which of the following statements about the continuity of f$($x$)$ at x$=1$ are true.

Select the correct answer below:

f$($x$)$ is not continuous at x$=1$ because it is not defined at x$=1.$

f$(1)$ exists, but f$($x$)$ is not continuous at x$=1$ because limx$1$f$($x$)$ does