Determine 𝑓 of one.
Here we see the function 𝑓 of 𝑥
is a piecewise function. We know this because it’s made up
of the graphs of two different functions. The first part of the graph is
defined over the interval from negative two to one. But of course, this empty circle
tells us that it’s not defined by this graph at this point. Then the second part of the
function is defined over the interval from one to eight. Once again, the empty dot tells us
that it’s not defined at 𝑥 equals one by this portion of the graph.
And so, how are we going to
determine 𝑓 of one? Well, we can’t. 𝑓 of one is totally undefined
according to our graph. There are plenty of values that we
can find. For example, 𝑓 of five is equal to
one, as is 𝑓 of negative one. But 𝑓 of one is completely
undefined according to our graph.