Piecewise Function Definition

Hi Mehtap, let's solve this piecewise function problem together. We are given a function f of x that behaves differently depending on the value of x.

Let's write down the definition of the function more formally. f of x equals five x squared minus two when x is less than three, and five x when x is greater than three.

Notice that the definition is split at x equals three. A common question for such functions is to find the limits from the left and right at this boundary point.

First, let's calculate the limit as x approaches three from the left, which we denote with a small minus sign.

To find this limit, we simply plug three into the quadratic expression. Three squared is nine.