What is the domain of this function: {(0, 1), (2, 3), (-1, 3), (4, 5)}?
Answers
Step-by-step explanation:
State the domain and range of the following relation. Is the relation a function?
{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}
I'll just list the x-values for the domain and the y-values for the range:
domain: {–3, –2, –1, 0, 1, 2}
range: {5}
This is another example of a "boring" function, just like the example on the previous page: every last x-value goes to the exact same y-value. But each x-value is different, so, while boring,
this relation is indeed a function.
In point of fact, these points lie on the horizontal line y = 5.
By the way, the name for a set with only one element in it, like the "range" set above, is "singleton". So the range could also be stated as "the singleton of 5"
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There is one other case for finding the domain and range of functions. They will give you a function and ask you to find the domain (and maybe the range, too). I have only ever seen (or can even think of) two things at this stage in your mathematical career that you'll have to check in order to determine the domain of the function they'll give you, and those two things are denominators and square roots.
Determine the domain and range of the given function:
\mathbf{\color{green}{\mathit{y} = \dfrac{\mathit{x}^2 + \mathit{x} - 2}{\mathit{x}^2 - \mathit{x} - 2}}}y=
x
2
−x−2
x
2
+x−2
The domain is all the values that x is allowed to take on. The only problem I have with this function is that I need to be careful not to divide by zero. So the only values that x can not take on are those which would cause division by zero. So I'll set the denominator equal to zero and solve; my domain will be everything else.
x2 – x – 2 = 0
(x – 2)(x + 1) = 0
x = 2 or x = –1
Then the domain is "all x not equal to –1 or 2".
The range is a bit trickier, which is why they may not ask for it. In general, though, they'll want you to graph the function and find the range from the picture. In this case:
graph