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The set of all x-values in a relation is called the?
domain
How do you find the domain of a relation given by a set of ordered pairs?
its the x coordinate (first number) It is the set of values that the x coordinate can take.
The domain of a relation is the set of all x-coordinates from each pair?
Yes.
Is a function a relation if and only the x-values do not repeat in a given set?
No. If an x-value is repeated but both values have the same image, you can still have a valid function. x values not repeating is not sufficient if there is no image. For example, consider 1/x and the domain as the integers -3, -2, -1, 0, 1, 2, 3. None of the x values repeats but there is no functional relationship because 1/x is not even defined for x = 0.
What is an inverse relationship between x and y?
That depends on the original relation. For any relation y = f(x) the domain is all acceptable values of x and the range, y, is all answers of the function. The inverse relation would take all y values of the original function, what was the range, and these become the domain for the inverse, these must produce answers which are a new range for this inverse, which must match the original domain. IE: the domain becomes the range and the range becomes the domain. Ex: y = x2 is the original relation the inverse is y = =/- square root x Rules to find the inverse are simple substitute x = y and y = x in the original and solve for the new y. The notation is the original relation if y = f(x) but the inverse is denoted as y = f -1(x), (the -1 is not used as an exponent, but is read as the word inverse)
