### Video Transcript

Determine the limit as π₯ tends to
two of the function represented by the graph.

Now, if we look at the graph, we
can see that the function is called π of π₯. And weβve being asked to find the
limit of π of π₯ as π₯ tends to two. In other words, this is the limit
as π₯ tends to two of π of π₯. This can also be described as the
value π of π₯ approaches as π₯ tends to two. So we need to find this value of π
of π₯ using our graph. We can consider what π of π₯ is
doing around the value of π₯ is equal to two. Weβll need to consider π of π₯ on
both the left and right of two. Letβs consider π of π₯ on the
right of π₯ is equal to two. We can see that as π₯ gets closer
and closer to two, π of π₯ is decreasing. And it is decreasing towards this
point here, which has a value of three. So we can say that as π₯ tends to
two from the right, the value of π of π₯ approaches three.

Letβs now consider what happens on
the left of π₯ is equal to two. We can again see that as π₯ gets
closer and closer to two, the value of π of π₯ is decreasing. And from the graph, we can see that
it is decreasing towards the same value that π of π₯ is approaching from the right
as π₯ approaches two. And thatβs a value of three. So now we can say that as π₯
approaches two from the left, π of π₯ approaches three. Since π of π₯ approaches the same
value from the left and the right of two, we can therefore conclude that the value
that π of π₯ approaches as π₯ tends to two is three. And so, we reach our solution,
which is that the limit as π₯ approaches two of π of π₯ is equal to three.