Given a real-world situation that can be modeled by a linear function or a graph of a linear function, determine and represent a reasonable domain and range of the linear function by using inequalities.
TEKS Standards and Student Expectations
A(2)(A ) determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range v alues for real‐world situations, both continuous and discrete; and represent domain and range using inequalities
Resource Objective(s)
Given a verbal statement or a graph of a linear function, determine its domain and range.
Essential Questions
Which variable is the independent variable?
Which variable is the dependent variable?
Vocabulary
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 1
A clown at a birthday party can blow up five balloons per minute. The relationship between the number of balloons inflated and the time that has passed can be expressed with the equation y = 5x, 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 example, the independent variable (x) is the number of minutes. The possible x-values include all real numbers greater than or equal to 0, since time can be measured in fractional parts of a minute.
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>.
