How To Find The Domain Of A Linear Function
Determining the Domain and Range for Linear Functions
Resources ID: A1M4L3
Grade Range: 9 - 12
Allow'south Get Started
Given a real-world situation that can exist modeled past a linear function or a graph of a linear function, determine and represent a reasonable domain and range of the linear part by using inequalities.
TEKS Standards and Student Expectations
A(2)(A ) determine the domain and range of a linear function in mathematical problems; decide reasonable domain and range v alues for real‐world situations, both continuous and detached; and represent domain and range using inequalities
Resources Objective(s)
Given a exact statement or a graph of a linear function, make up one's mind its domain and range.
Essential Questions
What is domain?
What is range?
Which variable is the independent variable?
Which variable is the dependent variable?
Vocabulary
- Independent Variable
- Dependent Variable
- Domain
- Range
Determining the Domain and Range Modeled by a Linear Role
To determine the domain of a given situation, identify all possible x-values, or values of the independent variable. To determine the range of a given situation, identify all possible y-values, or values of the dependent variable.
Example ane
A clown at a altogether party can blow up five balloons per minute. The relationship between the number of balloons inflated and the fourth dimension that has passed can be expressed with the equation y = fivex, where x is the number of minutes passed and y is the number of balloons inflated. Find the domain and range of the relations.
In this instance, the independent variable (x) is the number of minutes. The possible 10-values include all real numbers greater than or equal to 0, since fourth dimension tin can be measured in partial parts of a infinitesimal.
The dependent variable (y) is the number of balloons inflated. The possible y-values include all real numbers greater than or equal to 0.
Therefore, the domain is {x ≥ 0}, and the range is {y ≥ 0}.
DVD Rental Instance
An online DVD rental site charges a monthly membership fee of $10, plus $4 per DVD that is rented. The relationship between the number of DVDs rented and the total charge per month tin be expressed with the equation y = fourx + 10, where ten is the number of DVDs rented and y is the total charge per month. Observe the domain and range of this relationship.
In this example, the independent variable, x, is the number of DVDs rented. The possible 10-values include all whole numbers, since simply whole number of DVDs tin be rented.
The dependent variable, y, is the full charge per month. The possible y-values include 10, xiv, eighteen, 22, . . .
Therefore, the domain is {0,1,two,iii, . . .}, and the range is {10,xiv,18, 22, . . .}.
Determining the Domain from a Graph
Identify the set of all the x-coordinates in a office'due south graph to determine the domain.
In this case, the domain is {x≥ 0}, since 0 is the everymanx-value and the arrow indicates the line continues to the right. The boundary number of 0 is included, since the dot is solid.
Place the gear up of all the y-coordinates in the function'southward graph to decide the range.
In this instance, the range is {y≥ -2}, since -2 is the everymany-value and the arrow indicates the line continues upward. The boundary number of -two is included, since the dot is solid.
Another Case
Action i: Graphit Domain and Range
Click on the post-obit link to become to the interactive Graphit page.
- Enter the following functions into the y(x) box. Click "Plot/Update" and view the resulting graphs.
- Record the domain and range for each function in your OnTRACK Algebra Journal.
Function Domain Range The cost to park in a garage is a $5 entry fee plus $2 per hour. y(10) = 2x + v The amount of snow that fell later midnight is iii feet per 60 minutes. y(10) = 3x A swimming pool is draining at a charge per unit of 1.5 anxiety per minute. y(x) = -1.5ten
Activity ii: Matching Relationships to Domain and Range
Vocabulary Activity
Periodical Activeness
Source: https://texasgateway.org/resource/determining-domain-and-range-linear-functions#:~:text=To%20determine%20the%20domain%2C%20identify,will%20be%20your%20boundary%20numbers.
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