1.2 Lesson 6 Domain, Range, Set Builder Notation

Multiple Choice

Which of the following statements best describes a line in mathematics?

• A line is a straight path that extends infinitely in both directions.

• A line is a segment with two endpoints.

• A line is a curve that never crosses itself.

• A line is a path that stops at the edge of the graph.

Multiple Select

Based on the students' explanations and the graph of y = -4x + 7, which statements are correct?

• The graph cannot show the entire line.

• For any x-value, there will always be a y-value.

• The line will eventually stop at a certain x-value.

• The line extends infinitely in both directions.

Multiple Choice

What is the domain of a vending machine, as described in the example?

• The snacks that come out of the machine.

• The types and amounts of money the machine can accept.

• The number of buttons on the machine.

• The location of the vending machine.

Multiple Choice

Based on the definition of domain, what values can be used as an input for x if y = -4x + 7?

• all values greater than -5 and less than 5

• all values greater than -20 and less than 20

• it cannot be determined

• any value

Open Ended

Explain how the graph of y = -4x + 7 supports your answer about the domain of the function.

Multiple Choice

Based on the definition of domain, what values can be used as an input for x if 8x - 5y = 15?

• all values greater than -5 and less than 5

• all values greater than -20 and less than 20

• it cannot be determined

• any value

Multiple Choice

Which of the following statements best describes the y-values not included in the graphs of y = -4x + 7 and 8x - 5y = 15?

• Some y-values are not included because the graphs are lines.

• All y-values are included because for every x-value, there is a corresponding y-value.

• Only positive y-values are included.

• Only negative y-values are included.

Multiple Choice

Based on the definition of range, for the linear relationship 8x - 5y = 15, what values are outputs for y?

• all values greater than -10 and less than 15

• all values greater than -20 and less than 20

• it cannot be determined

• any value

Multiple Choice

Based on the definition of range, for a linear relationship y = -4x + 7, what values are outputs for y?

• all values greater than -10 and less than 15

• all values greater than -20 and less than 20

• it cannot be determined

• any value

Multiple Choice

How can the domain and range of all real numbers be represented using inequalities notation?

• -∞ < x < ∞ and -∞ < y < ∞

• 0 < x < ∞ and 0 < y < ∞

• -∞ < x ≤ ∞ and -∞ < y ≤ ∞

• x > 0 and y > 0

Open Ended

Why can't the domain −∞ < x < ∞ be written as −∞ ≤ x ≤ ∞?

Multiple Choice

What is the written description for the domain of the graph of y = -3/2x + 4 with a restricted domain?

• All values greater than or equal to -4 and less than or equal to 6.

• All values less than or equal to -4 and greater than or equal to 6.

• All values greater than or equal to -5 and less than or equal to 10.

• All values less than or equal to -5 and greater than or equal to 10.