Express the interval in set-builder notation and graph the interval on a number line (-6.2]
1 answer:
Answer:
{}
The number line is attached.
Step-by-step explanation:
By definition Set-builder notation is a mathematical shorthand used to provide specific details about a set.
In this case, you have the following interval:
You can obsseve that the left hand contains a parentheses, which means that -6 it is not included, then:
The right hand contains a bracket, which means that 2 is included:
The inequality is:
Therefore, in Set-builder notation this is:
{}
Observe the number line attached. Since -6 is not included, you must use an unfilled circle. Since 2 is included, you must use a filled circle.
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Answer: (1) d, f (2) c, d, f (3) e, f (4) a, b, c, d, f (5) e, f
<u>Step-by-step explanation:</u>
a) Natural Numbers: 1, 2, 3, ...
b) Whole Numbers: 0, 1, 2, 3, ... <em>(add zero to the Natural numbers)</em>
c) Integers: ..., -3, -2, -1, 0, 1, 2, 3, ... <em>(add negatives to the Whole numbers)</em>
d) Rationals: Add terminating and repeating decimals to Integers.
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e) Irrationals: Non-repeating decimals that are non-terminating. <em>This is its own category so cannot be a Rational number or above.</em>
f) Real Numbers: ALL of the above (a - e) are Real numbers.
1) -5.2 has a terminating decimal so it is a RATIONAL number.
2) -4 is below zero so is an INTEGER which means it is also a RATIONAL #
3) -4.3212... is a non-terminating decimal so it is an IRRATIONAL number
4) = 2 is a NATURAL number which means it is also a WHOLE number, INTEGER, and RATIONAL number.
5) is a non-terminating decimal so it is an IRRATIONAL number