Domain & Range

Multiple Select

Select all correct statements about the domain and range for the relation described: Domain is all real numbers greater than or equal to -1 and less than or equal to 3; Range is all real numbers greater than or equal to -2 and less than or equal to 4.

• The domain includes the value 0

• The range includes the value 5

• The domain includes the value -2

• The range includes the value 4

Multiple Choice

Which of the following best describes the domain of a function?

• The set of all possible output values

• The set of all possible input values

• The set of all numbers except zero

• The set of all values that make the function undefined

Open Ended

Why is it important to understand whether a relation is a function when studying algebra?

Open Ended

How can understanding patterns help us make more informed decisions, work efficiently, and understand the world around us?

Multiple Choice

Which of the following statements best describes the use of inductive reasoning in mathematics?

• It is used to prove mathematical theorems with absolute certainty.

• It helps us make conjectures based on observed patterns.

• It is only applicable to statistical data.

• It is used to solve equations directly.

Multiple Choice

Which of the following is NOT a function?

• Each input is paired with exactly one output.

• An input is paired with more than one output.

• Each element in the domain is paired with a unique element in the range.

• A relationship between two quantities.

Multiple Select

Select all the correct representations of a function from the options below:

• A table where each x-value has only one y-value.

• A graph where some x-values have multiple y-values.

• A set of ordered pairs with unique x-values.

• A mapping diagram where each input is paired with only one output.

Open Ended

Describe how multiple representations (equation, table, graph, words) can help you understand the behavior of a function.

Open Ended

How can you determine if a relation is a function when given a graph?

Multiple Choice

After removing which point from Relation H does it represent y as a function of x?

• (-4, 0)

• (-1, -7)

• (5, 4)

• (-3, -2)

Multiple Choice

After removing which point from Relation G does it represent y as a function of x?

• (-4, 0)

• (-1, -7)

• (5, 4)

• (-3, -2)

Multiple Choice

What is a common error students might make when plotting a point so that the resulting relation does NOT represent y as a function of x?

• Plotting a point with an x-coordinate of -3, -1, 1, or 2

• Plotting a point with a y-coordinate of -2, -1, 1, or 3

• Plotting a point with an x-coordinate of 0

• Plotting a point with a y-coordinate of 0

Multiple Select

Select all the sets of ordered pairs that could be from a function.

• {(1, 3), (3, 1), (6, 3)}

• {(-2, 0), (0, 0), (2, 0)}

• {(-2, 1), (3, 0), (-2, 3)}

• {(1, 2), (2, 4), (4, 8)}

Multiple Choice

Which set of ordered pairs could not be from a function?

• {(1, 3), (3, 1), (6, 3)}

• {(-2, 0), (0, 0), (2, 0)}

• {(-2, 1), (3, 0), (-2, 3)}

• {(1, 2), (2, 4), (4, 8)}

Open Ended

Explain how you can use the vertical line test to determine if a graph represents a function.

Multiple Choice

Which of the following graphs represents a function?

• A

• B

• C

• D

Multiple Choice

Which of the following tables represents a function?

• A

• B

• C

• D

Multiple Choice

Which of these ordered pairs could not lie on the graph of a function?

• A. (-1, 0); (-1, -1)

• B. (-1, 0); (1, -1)

• C. (-1, 1); (1, 0)

• D. (0, -1); (1, 1)

Multiple Select

Which representations can be used to show that a relation is a function? Select all that apply.

• Ordered pairs

• Mapping diagrams

• Graphs

• Tables

Multiple Choice

Which of the following statements about domain and range is correct?

• Domain refers to dependent values, range refers to independent values

• Domain refers to input values, range refers to output values

• Domain refers to values from bottom to top, range refers to values from left to right

• Domain refers to output values, range refers to input values

Open Ended

Explain how you can use the acronym 'DIX' and 'RDY' to remember the difference between domain and range.

Multiple Choice

Given the function g(x) = -(x - 7)^2 + 3, what is the range of g(x)?

• less than or equal to 7

• less than or equal to 3

• greater than or equal to 7

• greater than or equal to 3

Open Ended

Reflecting on today's lesson, what is one thing you learned about determining whether a relation is a function or identifying the domain and range of a function?