How do I write an interval notion and graph it...it is a set of real numbers that would be less than or equal to -4?

Answer 1

For an interval of numbers, two types of brackets are used, [] and (), the first signifies that interval includes the number before/after it and the latter indicate the interval includes everything upto that value.

e.g.

[0,2] indicates an interval of all real numbers from 0 to 2 including those numbers

(-1,6) indicates an interval of all real numbers between -1 and 6 but not -1 and 6 themselves

[5,12) indicates an interval of all real numbers from 5 upto but not including 12

and (-9,-2] indicates an interval of all real numbers from -2 down to but not including -9.

so, an interval of real numbers less than and equal to -4 would be (-­∞,-4], we use a ( for -∞ as, obviously, infinity can never be reached.

To graph line intervals, we use a solid line along the interval and use filled circles, •, to signify that the point it is on is included in the interval, and empty circles, ○, to signify the point it is on is not included in the interval. So an interval of [5,12) would be drawn like this,

•--------------------○

5 6 7 8 9 10 11 12

the drawing for (-­∞,-4] would simply be a straight solid line from the end of the negative side of the number line upto -4 with a • to show that -4 is included.