2A Domain & Range of Linear Functions

2A: determine the domain and range of a linear function; determine domain and range for real-world situations, both continuous and discrete;
and represent domain and range using inequalities

​RANGE: all possible y-values / output values
written from least to greatest

​Inequality Symbols:

< means less than

> means greater than

≤ means less than or equal to

≥ means greater than or equal to

​-∞ negative infinity
∞ positive infinity

​DOMAIN: all possible x-values / input values
written from least to greatest

Domain and Range of Discrete Functions

DISCRETE: “dots” / individual points NOT connected by a line

• Domain: list each x-value represented inside { } from least to greatest (do NOT repeat values)

• Range: list each y-value represented inside { } from least to greatest (do NOT repeat values)

​Domain: {-2, 0, 1, 3, 7}

Range: {-3, 1, 3, 4}

​Domain: {2, 3, 4, 5, 6, 7, 8}

Range: {1, 2, 3, 4, 7}

​(-1, 3), (2, 2), (-3, -2), (1, 5)





​Domain: {-3, -1, 1, 2}

Range: {-2, 2, 3, 5}

Multiple Choice

A florist is making bouquets of flowers for a wedding. Each bouquet will have 9 flowers. The graph shows the linear relationship between y, the number of flowers used, and x, the number of bouquets.

The florist will use no more than 8 bouquets for the wedding.

Which set best represents the domain of the function for this situation?

• {0, 2, 4, 6, 8, 10}

• {0, 1, 2, 3, 4, 5, 6, 7, 8}

• {0, 18, 36, 54, 72, 90}

• {0, 9, 18, 27, 36, 45, 54, 63, 72}

Multiple Choice

A coach has 96 golf balls for the school's golf team. The coach will give each player on the team 8 golf balls. The graph shows the linear relationship between y, the number of golf balls remaining for the team, and x, the number of players on the team.

The coach will use no more than 6 players on the school's golf team.

Which set best represents the range of the function for this situation?

• {96, 84, 72, 60, 48}

• {8, 9, 10, 11, 12, 13, 14}

• {48, 56, 64, 72, 80, 88, 96}

• {0, 1, 2, 3, 4, 5, 6}

CONTINUOUS: connected by a line

​Start and Stop (two dots)

Write as an inequality:

smallest # / inequality / x OR y / inequality / biggest #

​Start and NOT Stop (one dot and one arrow)

Write as an inequality: domain x ≤ 7

                                     range   y > -5

Or write in words: 

Domain: all real numbers less than or equal to 7

Range: all real numbers greater than -5

​NO Start and NO Stop

(arrows on BOTH ends of the line)

Write as an inequality: domain -∞ < x < ∞

                                     range   -∞ < y < ∞

Or write in words: all real numbers

CLOSED dots
use ≤ OR ≥

OPEN dots
use < OR >​

​

​

​Domain and Range of Continuous Functions

​Domain: x > -4
Range: y < 3

​​Domain: -2 ≤ x < 2
Range: -5 ≤ y < 3

​Domain: -∞ < x < ∞
Range: -∞ < y < ∞

​watch FIRST

​watch SECOND

Multiple Choice

Which graph best represents a function with a domain of all real numbers less than or equal to 6?

Multiple Choice

A part of linear function g is graphed on the grid.

Which inequalities best describe the domain and range of the part shown?

• Domain: -4 < x < 5

  Range: -7 < g(x) < 6

• Domain: -4 ≤ x ≤ 5

  Range: -7 ≤ g(x) ≤ 6

• Domain: -7 ≤ x ≤ 6

  Range: -4 ≤ g(x) ≤ 5

• Domain: -7 < x < 6

  Range: -4 < g(x) < 5

Drag and Drop

A part of a linear function is shown on the grid.



What is the range of the part of the linear function shown?



The range is the set of all real numbers ​

Placeholder

and ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

greater than -4

greater than -2

greater than or equal to -4

greater than or equal to -2

less than or equal to 2

less than or equal to 3

less than 2

less than 3

Multiple Choice

The domain and range of part of a linear function r are given:

x > 5

y < 2

Which graph could represent this part of linear function r?

Multiple Choice

A student worked out at a gym continuously for 50 minutes. The graph shows the remaining percentage of the workout as a linear function of x, the time in minutes.

Which answer choice best describes the domain and range of the function for this situation?

• Domain: all real numbers greater than or equal to 0 and less than or equal to 100

  Range: all real numbers greater than or equal to 0 and less than or equal to 50

• Domain: {-2}

  Range: {100}

• Domain: all real numbers greater than or equal to 0 and less than or equal to 50

  Range: all real numbers greater than or equal to 0 and less than or equal to 100

• Domain: {100}

  Range: {-2}

Drag and Drop

The graph of part of linear function g is shown on the grid.



Drag and drop the tiles to show the inequality that best represents the domain of the part shown.



​

Placeholder

​

Placeholder

​ ​

Placeholder

​​

Placeholder

​

Placeholder

Drag these tiles and drop them in the correct blank above

-9

<

x

≤

2

-6

3

g(x)

Dropdown

A student rode a bike from school to a recreation center. The graph shows the student's distance in miles from the recreation center after riding the bike for x minutes.



The range of this function for this situation is ​all real numbers

Select answer

and ​

Select answer

.

​Domain and Range of Real-World Situations

Determine the equation that represents the problem situation, y = mx + b.

• Domain is all possible input values (numbers that can be changed and plugged into the equation).

• Range is all possible output values (the result/answer when a value is plugged in for x).

​Lucy works in a diner making $12 per hour, not including tips. Whenever Lucy works, her shift ranges from 2 hours to 8 hours in one day. The total amount of money earned, y, having worked x total hours can be modeled using a linear function.
What is a reasonable domain and range for Lucy working one day?

​Equation: y = 12x
Domain: 2 ≤ x ≤ 8
Range: 24 ≤ y ≤ 96

​The Lady Raven Basketball Team is getting new uniforms this year! The total cost in dollars to buy uniforms can be found by the equation y = 35x + 50  where x is the number of uniforms purchased, and y is the total cost. There is a minimum of 12 players and maximum of 16 players on the team. What is the domain and range for this function?

​Equation: y = 35x + 50
Domain: {12, 13, 14, 15, 16}
Range: {470, 505, 540, 575, 610}

• ​$12 per hour indicates the slope of the equation; there's no y-intercept

• x represents hours; input # of hours for x continuous)

• y represents money earned; depends on the number of hours worked

• ​x represents the number of uniforms (players); discrete since you can't purchase a portion of a uniform

• y represents the total cost; depends on how many uniforms are purchased

Multiple Choice

The total cost in dollars to buy uniforms for the players on a volleyball team can be found using the function c = 34.95u + 6.25, where u is the number of uniforms bought. If there are at least 8 players but no more than 12 players on the volleyball team, what is the domain of the function for this situation?

• {8, 9, 10, 11, 12}

• 0 < u ≤ 12

• 0 < c ≤ 425.65

• {285.85, 320.80, 355.75, 390.70, 425.65}

Multiple Choice

A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs 20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pounds can be represented by f(x) = 20x + 4.

What is the range of the function for this situation?

• {0, 1, 2, 3, 4, 5, 6}

• {4, 24, 44, 64, 84, 104, 124}

• {0, 2, 4, 6}

• {4, 44, 84, 124

Multiple Choice

The daily cost of hiring a plumber, y, to work x hours on a repair project can be modeled using a linear function. The plumber charges a fixed cost of $80 plus an additional cost of $45 per hour. The plumber works a maximum of 8 hours per day.

For one day of work, what is the range of the function for this situation?

• 0 ≤ x ≤ 8

• 80 ≤ y ≤ 440

• 0 ≤ x ≤ 10

• 45 ≤ y ≤ 685