Given that x is an integer, state the relation represented by absolute value y = x/2 and 0 is less than or equal to x which is less than or equal to 2 by listing a set of ordered pairs. Then state whether the relation is a function. Write yes or no.
Please help--no clue what to do!
abs (x/2) is postive, so it is greater than zero. To be less than 2, that puts constraints on x, for instance, x cannot be six.
So a set of ordered pairs could be
(3, 3/2) and it would be a function.
To find a set of ordered pairs for the given equation, we need to substitute different values of x into the equation and calculate the corresponding values of y.
Let's start by substituting x = 0 into the equation:
y = 0/2
y = 0
The first ordered pair is (0, 0).
Next, let's substitute x = 1:
y = 1/2
The second ordered pair is (1, 1/2).
Lastly, substitute x = 2:
y = 2/2
y = 1
The third ordered pair is (2, 1).
Therefore, the set of ordered pairs for the equation y = x/2, where 0 ≤ x ≤ 2, is {(0, 0), (1, 1/2), (2, 1)}.
To determine whether the relation is a function, we need to check if each x-value has a unique corresponding y-value.
Looking at the set of ordered pairs, we can see that for each x-value, there is only one corresponding y-value. Hence, the relation is a function.
The answer is therefore: Yes, the relation is a function.