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.
Things You'll Need
- Graph paper (optional)
- Calculator (optional)
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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