Video Transcript
Which of the following figures
represents the interval left open, right closed from negative one to zero?
Now, when we read this
interval, we read it as left open, right closed. So if we say 𝑥 is an element
of this interval, then we’re saying 𝑥 can be greater than negative one. But it can also be less than or
equal to zero. Now, if we look at all of the
intervals represented on number lines, we do see that they do lie between
negative one and zero. In order to narrow this down
further then, let’s remind ourselves what the dots or circles at the end of each
interval mean. If we have an open or empty
dot, that means greater than or less than. Then, if we have a solid or
closed dot, that means we need to include the number that this lies above. So it means less than or equal
to or greater than or equal to.
In order to represent the
left-open right-closed interval from negative one to zero then, we need to have
an open dot at negative one and a closed dot at zero. Looking at each of the number
lines, we see that’s option (b). In fact, let’s go through and
represent the intervals for the remaining three number lines.
In example (a), we have an open
dot at each end. This means we have an open
interval from negative one to zero. Then, in option (c), we’re
looking at the opposite to option (b). It’s left closed, right
open. Finally in option (d), both of
our dots are closed. So we need to include both
negative one and zero in our interval. It’s the closed interval from
negative one to zero.
