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# Functions, Domain, and Range Study Guide (page 2)

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Updated on Oct 3, 2011

## Domain and Range

Earlier, we looked at the equation y =√x and stated that x could not be negative, because we cannot take the square root of a negative number. However, for the equation y = x, we could make x any real number. For this equation, we say that the domain is all real numbers. The domain of an equation or function is all the values that can be substituted for x. In the equation y =√x, the domain is zero and all positive real numbers.

While the domain describes what kind of x values can be put into an equation, the range tells us what kind of y values we will get back. In the equation y = x, because x can be any real number, y can be any real number. The range of y = x is all real numbers. The equation y =√x has a domain of zero and all positive real numbers, and the possible values of y are also zero and all positive real numbers. So the domain and range of this function are the same as well.

The domain and range are not always the same. The equation y = x2 has a domain of all real numbers, because any real number can be substituted for x. However, the square of any real number, including negative real numbers, is always positive. There will be no y values that are negative, so the range of y = x2 is zero and all positive real numbers.

What are the domain and range of ? The denominator of a fraction can never be 0, which means that x cannot be zero. The domain of the equation is all real numbers except 0. When these values are put into the equation, we can get back any y value except 0. The range of is all real numbers except 0.

#### Tip:

The value that makes a fraction undefined is often not only a value that must be excluded from the domain, but also a value that must be excluded from the range

Find practice problems and solutions for these concepts at Functions, Domain, and Range Practice Questions.

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