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.

Fill in the Blanks

The domain is the complete set of possible values of the

of a function or relation.

Fill in the Blanks

Fill in the blank: The domain is the complete set of possible values of the

of a function or relation.

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

Fill in the Blanks

What do the graphs of y - 3 = -4(x - 1) and 8x - 5y = 15 reveal about the domain and range of these linear relationships when the graph is zoomed out?

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 ≤ ∞?

Fill in the Blanks

Fill in the blank: The set-builder notation for the domain of the graph is {x:

≤ x ≤ 6}.

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.