Math Tip: Domain and Range of Functions

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[edit section] Finding Domains

1. If the function has division, find out where the denom. will equal zero. For example: (x^2 + 2x - 7)/(x - 3) has no value at x = 3 because the denom. equals zero.
2. If the function has a square root, find out where the square root part will have a negative value under the sign: f(x) = sqrt(x^2 - 7) has no value where x^2 < 7, so it has no value between -sqrt(7) and sqrt(7)
3. Combine both of the above qualities to find the domain. For example, if you cannot evaluate at 3 and you cannot evaluate from -4 to 4, then you just make the biggest set - from -4 to 4 (because 3 is included anyway)

[edit section] Finding Ranges

1. Plug in the domain. Find the minimum and maximum. If the function can become indefinitely big, it will be to positive infinity. Similarly, if it can become indefinitely small, it will be to negative infinity
2. If it has only absolute values or squares and square roots, it can never be negative
3. If it is a quotient and the numerator is constant, it can never be equal to 0