REPRESENT THE GIVEN INTERVAL ON THE NUMBER LINE

An open interval does not include its endpoints, and is enclosed in parentheses.

A closed interval includes its endpoints, and is enclosed in square brackets.

An interval is considered bounded if both endpoints are real numbers. An interval is unbounded if both endpoints are not real numbers.

Example 1 :

Graph the given interval on the number line.

(i)  (-∞, 5)

(ii)  [-2, 2)

(iii)  [-1, ∞)

(iv)  [-3, 0]

Solution :

(i)  (-∞, 5)

Converting the given interval notation as -inequality, we get

-∞ < x < 5

The possible values of x are greater than infinity but less than 5. (should not include 5).

(ii)  [-2, 2)

Converting the given interval notation as inequality, we get

-2 ≤ x < 2

The possible values of x are greater than or equal to -2 and less than 2.

(iii)  [-1, ∞)

Converting the given interval notation as inequality, we get

-1 ≤ x < ∞

The possible values of x are greater than or equal to -1 and less than infinity.

(iv)  [-3, 0]

Converting the given interval notation as inequality, we get

-3 ≤ x ≤ 0

The possible values of x are greater than or equal to -3 and less than or equal to 0.

Example 2 :

Describe and graph the interval of real numbers.

(i)  x ≤ 2

Solution :

Interval notation of given inequality is (-∞, 2].

The values which are less than or equal to 2 can be considered as solution.

By shading the possible solutions on the number line, we get

(ii)  -2 ≤ x < 5

Solution :

Interval notation of given inequality is [-2, 5).

The values which are greater than or equal to -2 and less than 5 can be considered as solution.

By shading the possible solutions on the number line, we get

(iii)  (-∞, 6)

Solution :

By writing the given interval using inequality, we get

-∞ < x < 6

The values which are greater than -infinity and less than 6 can be considered as solution.

By shading the possible solutions on the number line, we get

(iv)  [-3, 3]

Solution :

By writing the given interval using inequality, we get

-3≤< x ≤ 3

The values which are greater than or equal to -3 and less than or equal to 3.

By shading the possible solutions on the number line, we get

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