Lesson 10: Domain and Range (Part 1)

Domain and Range (Part 1)

5 min

Narrative

This Warm-up prompts students to consider possible input and output values for a familiar function in a familiar context. The work here prepares students to do the same in other mathematical contexts and to think about domain and range in the rest of the lesson.

Student Task

The total number of times a dog has barked is a function of the time, in seconds, after its owner tied its leash to a post and left. Less than 3 minutes after he left, the owner returned, untied the leash, and walked away with the dog.

Could each value be an input of the function? Be prepared to explain your reasoning.

15

$84\frac12$

300
Could each value be an output of the function? Be prepared to explain your reasoning.

15

$84\frac12$

300

Sample Response

15 and $84\frac12$ are possible inputs. The owner returned in under 180 seconds and then walked away with the dog, so 300 is not a possible input (assuming that the function is limited to the time the dog was tied to the leash and when the owner was away).
15 and 300 are possible outputs, but $84\frac12$ is not because it is not possible for the dog to bark a fractional number of times.

Activity Synthesis (Teacher Notes)

Invite students to share their responses and reasoning. Highlight explanations that make a convincing case for why values beyond 180 could not be inputs for this function and why fractional values could not be outputs.

Some students may argue that 300 could be an input because "300 seconds after the dog's owner walked away" is an identifiable moment, even though the dog and its owner have walked away and may no longer be near the post. Acknowledge that this is a valid point, and that it highlights the need for a function to be more specifically defined in terms of when it "begins" and "ends." If time permits, solicit some ideas on how this could be done.

Tell students that in this lesson, they will think more about values that make sense as inputs and outputs of functions.

Standards

Addressing

F-IF.5·Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
F-IF.5·Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
F-IF.5·Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
F-IF.5·Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
F-IF.5·Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
F-IF.5·Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
HSF-IF.B.5·Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function $h(n)$ gives the number of person-hours it takes to assemble $n$ engines in a factory, then the positive integers would be an appropriate domain for the function.

20 min

10 min

Knowledge Components

All skills for this lesson

No KCs tagged for this lesson

Domain and Range (Part 1)

5 min

Narrative

Student Task

Could each value be an input of the function? Be prepared to explain your reasoning.

15

$84\frac12$

300
Could each value be an output of the function? Be prepared to explain your reasoning.

15

$84\frac12$

300

Sample Response

15 and $84\frac12$ are possible inputs. The owner returned in under 180 seconds and then walked away with the dog, so 300 is not a possible input (assuming that the function is limited to the time the dog was tied to the leash and when the owner was away).
15 and 300 are possible outputs, but $84\frac12$ is not because it is not possible for the dog to bark a fractional number of times.

Activity Synthesis (Teacher Notes)

Tell students that in this lesson, they will think more about values that make sense as inputs and outputs of functions.

Standards

Addressing

F-IF.5·Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
F-IF.5·Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
F-IF.5·Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
F-IF.5·Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
F-IF.5·Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
F-IF.5·Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
HSF-IF.B.5·Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function $h(n)$ gives the number of person-hours it takes to assemble $n$ engines in a factory, then the positive integers would be an appropriate domain for the function.

Domain and Range (Part 1)

Warm-upNumber of Barks5 minKCs

Narrative

Student Task

Sample Response

ActivityCard Sort: Possible or Impossible?20 minKCs

ActivityWhat about the Outputs?10 minKCs

Knowledge Components

Domain and Range (Part 1)

Warm-upNumber of Barks5 minKCs

Narrative

Student Task

Sample Response

ActivityCard Sort: Possible or Impossible?20 minKCs

ActivityWhat about the Outputs?10 minKCs

5 min

20 min

10 min

5 min

20 min

10 min