Video Transcript
Which graph represents the function
𝑓 of 𝑥 equals log base five of 𝑥?
And we have five graphs to choose
from. So, let’s begin by inspecting the
function we’ve been given. It’s a logarithmic function, and it
has the general form of the logarithmic function 𝑓 of 𝑥 equals log base 𝑛 of 𝑥
where, of course, our value of 𝑛, which is here five, cannot be equal to one and is
greater than zero. Now, one of the features we know
about this function is that it passes through the 𝑥-axis at one, but it also passes
through the point 𝑛, one. So we’re looking for a graph which
passes through one, zero and five, one. We also know that the 𝑦-axis or
the line 𝑥 equals zero is an asymptote to this graph. In other words, the graph of our
function approaches the 𝑦-axis but never actually reaches it. And we know that when 𝑛 is greater
than one, the graph itself is purely increasing. It’s increasing over the entire
domain of the function.
Well, in fact, all of our graphs,
if we look carefully, are increasing and they all have the 𝑦-axis as an
asymptote. So we need to identify which of our
graphs pass through the point one, zero and five, one. In fact, if we plot each of these
points on every single graph, we see that only one graph passes through both
points. The correct graph, then, is
(A). Graph (A) represents the function
𝑓 of 𝑥 equals log base five of 𝑥.
