… how range and domain work right …
Hi sebastians. Are you asking for a definition of Domain and Range? (I'm not sure what you mean by saying, "work right".)
Domain and Range are each a set of numbers.
Let's say we have a relationship between numbers x and y, like the linear equation
y = 5x + 1
The Domain is the set of all possible Real numbers that we could substitute for x, to obtain a Real number for y.
The Range is the set of all the resulting y-values.
(If you're familiar with the vocabulary of 'functions', then the Domain is the set of all possible inputs, and the Range is the set of all corresponding outputs.)
For another example, if we look at the relationship y = 1/x, then we're allowed to replace x with any Real number except zero (we may not divide by zero). Therefore, the Domain is the set of all Real numbers except zero. The Range is the set of all the corresponding y-values that result, when the numbers in the Domain are substituted for x.
If we look at y = sqrt(x), then the Domain is the set of all non-negative Real numbers (in the Real number system, we may not take the square root of negative numbers). The Range is the set of all corresponding y-values.
In my first and third examples, the Range is the same set as the Domain (check out the graphs).
On the xy-plane, any graph where y depends on x consists of plotted (x,y) points. All of those x-values comprise the Domain. All of those y-values comprise the Range.
Do you have a specific exercise, for which you need help? If so, please post the entire exercise, along with your thoughts and any work you've done, and we'll go from there.
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