Intervals of Real Numbers

Definition of an Open Interval

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The open interval \((a, b)\) consists of all real \(x\) such that:

a ≤ x ≤ b

a < x < b

a ≤ x < b

a < x ≤ b

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Definition of a Closed Interval

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The closed interval \([a, b]\) includes:

Only the left endpoint

Neither endpoint

Only the right endpoint

Both endpoints

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Identify the Unbounded Intervals

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Select every interval below that is unbounded (contains the symbol ∞).

(−∞, b]

(a, b)

(a, ∞)

[a, b]

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Is [a, +∞) Open or Closed?

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Is the interval \([a, +\infty)\) considered open, closed, or neither?

Both open and closed

Open

Neither open nor closed

Closed

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The Half-Open Interval (a, b]

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The half-open interval \((a, b]\) is:

Open at a, closed at b

Closed at both ends

Closed at a, open at b

Open at both ends

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Domain of a Square Root Expression

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For what values of \(x\) is \(\sqrt{12 - x}\) a real number?

x < 12

x ≥ 12

x > 12

x ≤ 12

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Domain of Another Square Root Expression

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For what values of \(x\) is \(\sqrt{16 - x^2}\) a real number?

x ≥ 4

−4 ≤ x ≤ 4

x ≤ −4

−4 < x < 4

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Domain of a Rational Function

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The function \(f(x) = \dfrac{1}{x - 2}\) is defined for which set of x-values?

All real numbers

(−∞, 2) ∪ (2, ∞)

x > 2 only

x < 2 only

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Sort the Intervals: Bounded or Unbounded?

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Intervals

×[0, ∞)

×[−3, 5]

×(1, 9]

×(2, 7)

×(−∞, ∞)

Bounded

Unbounded

Classify each interval as Bounded or Unbounded

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Definition of an Open Interval

Correct Answer

Explanation

Definition of a Closed Interval

Correct Answer

Explanation

Identify the Unbounded Intervals

Correct Answer

Explanation

Is [a, +∞) Open or Closed?

Correct Answer

Explanation

The Half-Open Interval (a, b]

Correct Answer

Explanation

Domain of a Square Root Expression

Correct Answer

Explanation

Domain of Another Square Root Expression

Correct Answer

Explanation

Domain of a Rational Function

Correct Answer

Explanation

Sort the Intervals: Bounded or Unbounded?

Classify each interval as Bounded or Unbounded

Classify each interval as Bounded or Unbounded

Correct Answer

Explanation

Quran Recitation

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