Exploring Domain, Range, and Interval Notation

The video tutorial introduces the concepts of domain and range, explaining how they represent input and output values in functions. It introduces interval notation as a concise way to express these values, using parentheses and brackets to indicate whether endpoints are included. The tutorial provides examples and uses graphs to illustrate how domain and range are applied in different scenarios. It also covers graphing linear equations with specific domains and explores compound domains. The video concludes with a recap of the importance of understanding these concepts, especially in preparation for more advanced algebra courses.

What is the domain of a function?

• The set of all input values

• The set of all y-values

• The set of all z-values

• The set of all output values

In interval notation, what do parentheses indicate?

• Including the end values

• Excluding the end values

• Including only the first value

• Including only the second value

How would you write the domain of all x-values between -1 and 5, excluding -1 and 5, in interval notation?

• (-1, 5]

• [-1, 5)

• (-1, 5)

• [-1, 5]

What does a square bracket in interval notation signify?

• Including only the first value

• Excluding the end values

• Including the end values

• Including only the second value

How is infinity represented in interval notation?

• With square brackets

• With parentheses

• With curly braces

• With angle brackets

If a graph continues indefinitely to the left, what is the domain in interval notation?

• (-∞, y)

• (-∞, x]

• (-∞, 0)

• (-∞, ∞)

For the function y = 1/2x + 2 with a domain from -2 to 4 inclusive, what is the range?

• [1, 5]

• [2, 5]

• [2, 4]

• [1, 4]

In the graph of y = -x - 5 with a domain from -4 to 4, what type of points are at x = -4 and x = 4?

• Open circles at -4 and solid dots at 4

• Solid dots at -4 and open circles at 4

• Open circles

• Solid dots

What is the range of the function y = -x - 5 with a domain from -4 to 4?

• [-9, -1]

• (-9, -1]

• [-9, -1)

• (-9, -1)

What does the union symbol (U) represent in interval notation?

• Not

• If

• Or

• And