Question 1

Which of the following represents the interval that includes all real numbers greater than or equal to $$a$$ and less than $$b$$?

Accepted Answer

$$[a, b)$$

Question 2

What is the set-builder notation for the interval $$(-\infty, b]$$?

Accepted Answer

$$\{ x \mid x \leq b \}$$

Question 3

Which interval notation describes all real numbers except for $$a$$ and $$b$$?

Accepted Answer

$$(a, b)$$

Question 4

If a chemical reaction is only possible when the temperature $$T is $$between $$20^\	ext{o}C$$ and $$80^\	ext{o}C$$, inclusive, which interval notation best describes the possible temperatures?

Accepted Answer

$$[20, 80]$$

Question 5

Which of the following intervals is represented by the graph of a line starting at $$a ($$open circle) and extending to the right without bound?

Accepted Answer

$$(a, \infty)$$

Question 6

A medication is effective for patients whose age $$x$$ satisfies $$x \geq 18. $$Which interval notation describes the ages for which the medication is effective?

Accepted Answer

$$[18, \infty)$$

Question 7

Which interval includes all real numbers except $$b$$, but includes $$a$$?

Accepted Answer

$$[a, b)$$

Question 8

If $$x is a $$real number such that $$x \u003e a$$, which interval notation represents all possible values of $$x$$?

Accepted Answer

$$(a, \infty)$$

Question 9

Which of the following is the correct set-builder notation for the interval $$[a, b]$$?

Accepted Answer

$$\{ x \mid a \leq x \leq b \}$$

Question 10

A company only hires employees aged strictly between 21 and 65. Which interval notation best describes the eligible ages?

Accepted Answer

$$(21, 65)$$

Question 11

Which interval notation represents all real numbers less than $$b$$?

Accepted Answer

$$(-\infty, b)$$

Question 12

If $$x is a $$real number such that $$x \leq a$$, which interval notation represents all possible values of $$x$$?

Accepted Answer

$$(-\infty, a]$$

Foundations of College Algebra: Sets, Properties, Notation, and Operations

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