How to Find the Domain in Math

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A function is any equation where values of one variable influence a second variable. The domain of a function in math is all possible values for "x", the independent variable, while the range is all possible values for a second unknown, "y", the dependent variable. To solve for the range, solve for the domain first.

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  • Eliminate all numbers that make the value under the square root sign yield a negative number. In domain problems, real numbers are the only correct answers. When considering the function, y=√(x-16), try the value zero in the function and calculate what the number under the square root sign would be, if you made "x" a zero. Zero subtract 16 equals a (-16) and you cannot have a negative value under the square root sign. You can, therefore, eliminate zero and all values less than zero -- the negative numbers.

  • Try positive numbers greater than zero. A positive value of at least 16 is necessary in the function y=√(x-16) to yield a positive number under the square root sign. The domain of the function, y=√(x-16) is therefore, "numbers greater than or equal to 16." In math notation this is written as x=≥16.

  • Eliminate all numbers that make the denominator of a fraction zero. In considering the function, y=1+10/x+10, putting the value of zero in the denominator of the fraction, would not result in making the denominator zero, so zero is an acceptable value.

  • Try negative numbers in the equation.The number (-10) in the bottom of the equation makes the denominator a zero, making (-10) unacceptable.

  • Try positive numbers. Every positive number would be acceptable. Therefore for this function the domain is "all numbers except (-10)". In math notation this is written as x≠(-10).

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