determine whether this relation is a function, state its domain and range, is it continuous or discrete.
{(-3,0), (-1,1), (0,1), (4,5), (0,6)}
if any two pairs have the same 1st element, it is not a function
domain is the set of 1st elements, range, of the 2nd
continuous if defined over an interval, otherwise discrete.
so, whaddaya think?
is a function?
No. two pairs start with zero.
f(0) cannot be both 1 and 6.
stop guessing.
how do i get the domain and range
1st step - read what I wrote above.
I assume you can tell which number in each pair is the 1st or 2nd.
Take a look at your text - I'm sure it explains it
try google "relation domain" or something
To determine if a relation is a function, we need to check if each input (x-value) in the set of ordered pairs corresponds to exactly one output (y-value). In this case, let's examine the given relation:
{(-3,0), (-1,1), (0,1), (4,5), (0,6)}
To see if it is a function, we need to check if each x-value (the first value in each pair) appears only once. In this case, all the x-values are unique, which means it passes the vertical line test and is indeed a function.
The domain of a function is the set of all possible x-values, which, in this case, would be {-3, -1, 0, 4}. These are all the x-values present in the given ordered pairs.
The range of a function is the set of all possible y-values. To determine this, we need to consider all the y-values (the second value in each pair), which are {0, 1, 5, 6}. These are all the y-values present in the given ordered pairs.
Regarding the question of whether the relation is continuous or discrete: A continuous function is one where the graph does not have any breaks or gaps. On the other hand, a discrete function has isolated points. In this case, we can see that the relation consists of specific points, and there are no connected intervals between them. Thus, the relation is discrete.
Summary:
- The given relation is a function as each x-value corresponds to only one y-value.
- The domain is {-3, -1, 0, 4}.
- The range is {0, 1, 5, 6}.
- The relation is discrete.