Understanding Interval Notation

The video tutorial introduces interval notation as a method to express sets of points, transitioning from set notation and graphing. It explains open and closed intervals, how to graph inequalities, and how to convert these graphs into interval notation. The tutorial provides examples to illustrate the concepts, emphasizing the importance of using correct symbols for open and closed intervals, and the use of infinity in interval notation.

What is the primary goal of using interval notation?

• To graph linear equations

• To simplify complex equations

• To represent sets of points in a concise way

• To solve algebraic expressions

How is an open interval represented in interval notation?

• Using angle brackets

• Using rounded parentheses

• Using curly braces

• Using square brackets

What does a closed interval include that an open interval does not?

• None of the above

• Only one endpoint

• The midpoint

• The endpoints

When dealing with infinity in interval notation, which symbol is always used?

• Angle brackets

• Rounded parentheses

• Curly braces

• Square brackets

In interval notation, how is the interval from negative infinity to a number represented?

• Using rounded parentheses

• Using square brackets

• Using angle brackets

• Using curly braces

How would you write the interval that starts at -1 and goes to +2, including -1 but not 2?

• (-1, 2]

• [-1, 2)

• (-1, 2)

• [1, 2]

What is the interval notation for a set that goes from negative infinity to 4, not including 4?

• [∞, 4]

• (-∞, 4)

• (-∞, 4]

• [∞, 4)

How is the interval -2 < x ≤ 3 represented in interval notation?

• [-2, 3]

• (-2, 3)

• (-2, 3]

• [-2, 3)

What does the union symbol in interval notation represent?

• The midpoint of an interval

• The intersection of two intervals

• The combination of two distinct intervals

• The exclusion of a point from an interval

How would you express the interval for x < -2 or x > 1 using interval notation?

• (-∞, -2) ∪ (1, ∞)

• [-∞, -2] ∪ [1, ∞]

• (-∞, -2) ∩ (1, ∞)

• [-∞, -2] ∩ [1, ∞]