Video Transcript
Determine 𝑓(0) using the graph.
Let’s look at the graph of our
function. It must be a piecewise function,
and this is because it’s made up of pieces of graphs of various functions over
various intervals on 𝑥. For instance, let’s take the first
portion of graph here. This portion is defined by a
specific function over the interval from negative 10 to eight. In fact, we could even define this
as the left-closed, right-open interval. And that’s because the solid dot
tells us that it’s defined at 𝑥 equals negative 10 but not defined by this part of
the function at 𝑥 equals negative eight. Then, the second part of the
function allows us to define 𝑓 of 𝑥 at 𝑥 equals negative eight with the solid dot
here.
But when 𝑥 is equal to zero, we
can’t use this part of the graph to determine 𝑓 of zero. The empty dot tells us it’s not
defined by this part of our function. So, how are we going to determine
𝑓 of zero? Well, when 𝑥 is zero, we’re
looking for a part of the function that lies on the 𝑦-axis. We’ve already seen this can’t be
defined by this function here, but we do have a solid dot here. And so, the function is actually
defined when 𝑥 is equal to zero. This point has coordinates zero,
four. So we see that 𝑓 of zero must be
equal to four.
