Question

Question #fab0a

Answer 1

domain = function input
range = function output

Explanation:

Say you have a function y=f(x). Your domain is x, and your range is y. Domain is what you can input into a equation. Range is the output of a function. The domain and range can be all real numbers, but there are functions that can restrict the domain or range.

For typical polynomials, the domain is all real numbers. The range can vary though. You have to look at the leading term, which I am referring to the polynomial with the greatest exponent. If the leading term is `x^n` (where n = 1, 3, 5, 7,...), your range is all real numbers. If the polynomial is a quadratic, your range is y ≥ minimum or y ≤ maximum of the quadratic.

If you are working with the square root function, your radicand (what is under the (`sqrt`) radical symbol) must be ≥ 0. Your range will always be ≥ 0. There is an exception to this though. If you see `±sqrt`, then your range is all real numbers.

With trigonometric functions, the domain is all real numbers. The range is restrictive, but it depends on the function. Is you use cosine and sine, the range is dependent on the amplitude of the function. The other four trigonometric functions have many asymptotes, so the range cannot be certain numbers. Asymptotes are lines that approach, but never touch, a function.

There are more types of equations, such as exponential, logarithmic, and rational functions. All of these ran have limited domains and ranges, depending on the function in question.

If you have a graphing calculator, try out random functions to see what the domain and range can be.