Question Video: Identifying the Number Line That Represents a Given Interval | Nagwa Question Video: Identifying the Number Line That Represents a Given Interval | Nagwa

# Question Video: Identifying the Number Line That Represents a Given Interval Mathematics • Second Year of Preparatory School

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Which of the following figures represents the interval (−1, 0]?

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### 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.

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