Question

NO LINKS!!!

Consider the interval.
(-∞, 9]
State whether the interval is bounded or unbounded.
a. bounded
b. unbounded
Represent the interval with an inequality
a. x > 9
b. x≥ 9
c. x≥-9
d. x < 9
e. x ≤ 9
Sketch the graph

Answer 1

b. unbounded

e. x ≤ 9

Explanation:

Interval notation

( or ) : Use parentheses to indicate that the endpoint is excluded.

[ or ] : Use square brackets to indicate that the endpoint is included.

A bounded interval is an interval that includes both its endpoints.

For the interval (-∞, 9]:

• The endpoint -∞ is not included.
• The endpoint 9 is included.

Therefore, the given interval is unbounded.

Inequality notation

• < means "less than"
• > means "more than"
• ≤ means "less than or equal to"
• ≥ means "more than or equal to"

Therefore, the given interval is represented by the inequality x ≤ 9.

To sketch the graph on a number line:

• Place a closed circle at 9.
• Shade to the left of the closed circle.

To sketch the graph on a coordinate plane:

• Plot a solid line at x = 9.
• Shade to the left of the line.

Answer 2

a. unbounded

e. x ≤ 9

Explanation:

The interval means all real numbers less than or equal to 9.

Since all numbers to negative infinity are included, it is unbounded.

a. unbounded

e. x ≤ 9

A sketch looks like a number line with a solid dot at 9 and an line pointing left with an arrowhead at the left pointing left.