The figure shows an interval on the number line. Write an expression for it using interval notation.
The first thing we need to consider is actually all the notation before we actually solve this problem. The first notation we’re looking at is actually the notation on a number line itself. First of all, we’re gonna look at so the dots or circles. If we have a filled-in circle, this means that actually the value that the circle is actually on is included. So if it’s filled-in, it’s an included value. However, if the circle isn’t filled-in, then we know that that value is going to be excluded. So it excludes that value.
Okay, so that’s what the dots or circle mean. And if we had just an arrow, this would mean the values would continue. I’ve drawn a little diagram here to help show it. If we had this open circle and then the arrow pointing to the right, from two, what this would mean is it would mean all the values greater than two but not including two. Right. So now we actually know what the signs mean on the number line. We can see which values we’re gonna be looking at in our question.
Well, I’m gonna call our number 𝑥. So therefore, looking at our number line, we could say that 𝑥 is greater than or equal to negative three and less than or equal to one. And we know it’s less than or equal to and greater than or equal to because we’ve actually got filled-in circles. Okay, great. But we haven’t finished the question there because our question asked us to write it in interval notation. So let’s take a look at interval notation.
So first of all, if we have a bracket, so here we’ve got a bracket 𝑎, then this means that we’re actually gonna include the value 𝑎. So that means including the value 𝑎. However, if we have a reversed bracket, so we’ve got reversed bracket 𝑎, or a parenthesis and 𝑎, then this means we’re actually gonna be excluding value 𝑎. Okay, so now we know our interval notation. Let’s write our interval using that.
So therefore, we can say that using this interval notation, we can actually write the interval on our number line as open bracket, negative three, one, close bracket.
And recapping, the reason we actually have the brackets is because looking back at our number line, we had the closed circle which means that we include the values negative three and one.