How To Solve Domain Problems

Wolfram|Alpha is a great tool for finding the domain and range of a function.It also shows plots of the function and illustrates the domain and range on a number line to enhance your mathematical intuition.

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Unless a linear function is a constant, such as f(x) = 2, there is no restriction on the range. Since a quadratic function has two mirror image halves, the line of reflection has to be in the middle of two points with the same y value.

The vertex must lie on the line of reflection, because it’s the only point that does not have a mirror image!

Since it is impossible to divide by zero, the denominator of a fraction cannot equal zero.

Therefore, for the fraction 1/x, the domain is “all numbers not equal to zero,” since the denominator cannot equal zero.

It also doesn’t mean that all real numbers can be function values, f(x). The restrictions partly depend on the type of function.

could happen whenever the function has a variable in the denominator of a rational expression.

For example, if x = −4, then −x = −(−4) = 4, a positive number.

Remember, here the range is restricted to all real numbers.

The domain of a fraction refers to all real numbers that the independent variable in the fraction can be.

Knowing certain mathematical truths about real numbers and solving some simple algebra equations can help you find the domain of any rational expression. The denominator is the bottom number in the fraction.


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