Please give an example of a function and how to find its domain and range. Please make it as detailed as possible!
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A function is any equation that has no more than one output for each input. For simplicity's sake, I'll keep it with just "x" and "y". Here, "x" is your independent variable, or the input. "y" is your dependent variable, or output.
y=x is one of the simplest two variable function around. Choose any number and plug it in for "x", and "y" will equal that same number. eg. if we let x=1, then y=1 (given the function y=x). Note that we can never have more than one value for y given a particular x (for example, if x=1, y cannot be 1 and 2).
The domain of a function (D) is defined as the set of all possible inputs. So for a function with only "y" and "x", the domain will be all numbers that "x" can be. For y=x, x can be anything -∞ to ∞.
Another example is y=2x/x. While it may seem that by simplifying, y=2 (divide the x), in reality there will be a "hole" at the point x=0 since you cannot divide by 0! That is the only restriction in this case, so here, domain is (-∞, 0), (0, ∞). This is read as "the domain of the function is negative infinity to 0 non-inclusive, and 0 (non-inclusive) to infinity".
The range of a function (R) is defined as the set of all possible outputs. So for a function with only "y" and "x", the domain will be all numbers that "y" can be. For y=x, y can be anything -∞ to ∞.
For the function y=2x/x, we can find that no matter what number you plug into for "x", whether it be 1, 10, -9999, or √84, y can only be 2. Therefore, the range of this function is 2, or [2].
For the function y=x^2, we find that no matter what values are plugged in for "x", the output "y" will always be greater or equal to 0. Here, the range is [0, ∞), read as "the range is 0 inclusive to infinity".
y=x is one of the simplest two variable function around. Choose any number and plug it in for "x", and "y" will equal that same number. eg. if we let x=1, then y=1 (given the function y=x). Note that we can never have more than one value for y given a particular x (for example, if x=1, y cannot be 1 and 2).
The domain of a function (D) is defined as the set of all possible inputs. So for a function with only "y" and "x", the domain will be all numbers that "x" can be. For y=x, x can be anything -∞ to ∞.
Another example is y=2x/x. While it may seem that by simplifying, y=2 (divide the x), in reality there will be a "hole" at the point x=0 since you cannot divide by 0! That is the only restriction in this case, so here, domain is (-∞, 0), (0, ∞). This is read as "the domain of the function is negative infinity to 0 non-inclusive, and 0 (non-inclusive) to infinity".
The range of a function (R) is defined as the set of all possible outputs. So for a function with only "y" and "x", the domain will be all numbers that "y" can be. For y=x, y can be anything -∞ to ∞.
For the function y=2x/x, we can find that no matter what number you plug into for "x", whether it be 1, 10, -9999, or √84, y can only be 2. Therefore, the range of this function is 2, or [2].
For the function y=x^2, we find that no matter what values are plugged in for "x", the output "y" will always be greater or equal to 0. Here, the range is [0, ∞), read as "the range is 0 inclusive to infinity".
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