How to Determine Practical Domain and Range

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A function is a mathematical relationship where a value of "x" has one value of "y." Though there can only be one "y" assigned to an "x," multiple "x" values can be attached to the same "y." The possible values of "x" is called the domain. The possible values of "y" is called the range. Theoretical domains and ranges deal with all possible solutions. Practical domains and ranges narrow the solution sets to be realistic within defined parameters.

    Create a function equation from a word problem that includes information that will define the practical domain and range. Use this problem as an example: Anna is going to babysit for the Smith family, who agreed to give her $10 just for showing up to the house and $2 per hour she stays, for up to 10 hours. How much will Anna earn total? Note that there are supposed to be two variables. Use the total earned as "y," the unknown number of hours Anna works as "x," 10 dollars as the constant and $2 as the coefficient on "x": y = 10 + 2x.

    Define the domain according to the values possible for "x": Anna can only babysit a maximum of 10 hours but could also babysit 0 hours since she only needs to show up to collect the $10. Write the domain in terms of an inequality: 0 ≤ x ≤ 10.

    Place the low and high values into the function to solve for "y" and determine the minimum and maximum values for the practical range. Solve with 0: y = 10 + 2(0) = 10. Solve with 10: y = 10 + 2(10) = 30. Write the range in terms of an inequality: 10 ≤ x ≤ 30.


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