I'm totally lost on this discussion question for my math class. Any help?
What is the difference between domain and range? Provide an example of at least five ordered pairs that do not model a function. The domain will be any five integers between 0 and 20. The range will be any five integers between -10 and 10. Your example must not be the same as those of other students or the textbook. Why does your example not model a function?
The answer to the question lies in the definition of a function, which is a transformation from a set X of values to a set Y of values, such that any value in the set X will be transformed to one and only one value in the set Y.
An ordered pair (x,y) represents one particular element x in the set X that will be transformed into an element y in the set Y.
The formal notation is
y = f(x), where x∈X and y ∈Y.
The set X is called the domain, and contains all valid values of x. The set Y is called the range, and contains all possible values of y.
An example of a function is
y = f(x) = x², and some ordered pairs are: (-1,1), (0,0), (1,1), (2,4), (3,9).
Note that even though some values of y have been duplicated, the same value of x always give one and only one value of y.
If we had a relation such as
y = sqrt(x),
we would have ordered pairs such as
(0,0), (1,1), (1,-1), (4,2), (4,-2).
In this case, since y=±sqrt(x), the same value of x is not transformed to one single value of y, and so sqrt(x) is NOT a function.
Take it from here and post your answer for a check if you wish.
the domain is all of ur x values and the range is ur y values
a set of ordered pairs is a function if it passes the vertical line test, which means you can draw a vertical line anywhere on the line and it wont cross two points. the way a set would be a function is if all of the x values are different
Of course! I'd be happy to help you with your math question.
Firstly, let's start with the difference between domain and range. In mathematics, the domain of a function is the set of all possible input values, also known as the x-values. It represents the values for which the function is defined. The range, on the other hand, is the set of all possible output values, also known as the y-values. It represents all the values that the function can take.
To provide an example of five ordered pairs that do not model a function, we need to make sure that each input (domain) value is associated with only one output (range) value. If there exists any input value that is associated with more than one output value, then the example would not be a function.
Here's an example of five ordered pairs that do not model a function:
(1, 2)
(2, 4)
(3, 6)
(4, 8)
(1, 10)
In this example, we can see that the input value of 1 is associated with two different output values, namely 2 and 10. Since the input value of 1 is not associated with a unique output value, this example does not represent a function.
To avoid duplicating examples from other students or the textbook, you can choose any other five integers between 0 and 20 for the domain, and any five integers between -10 and 10 for the range. Just make sure that each input is associated with only one output value.