To find:the domain of the given relation and draw the function also whether the relation is a function or not.
Answer to Problem 18WE
The domain of relation is
Explanation of Solution
Given information:
The relation is
Definition used:
A function is relation in which different ordered pairs has different first coordinates.
Result used:
Vertical line test:
A relation is a function if and only if no vertical line intersects its graph more than once.
Calculation:
It is given that the relation is
The term
Note that, the modulus of x defines as
By using the definition of the modulus,
If the value of
The value of x and y are integers, so the value of x cannot be 0, more than 2 and less than
Thus, the only possible values of x are
The ordered pairs of the elements are
If the value of
The ordered pairs of the elements are
Thus, the relation is a set of ordered pairs as listed below,
{
Note that, the domain of the relation is a set of first coordinates in the ordered pairs.
Therefore, the domain of relation is
A function is relation in which different ordered pairs has different first coordinates.
Here, the different ordered pairs
Therefore, the given relation
Graph:
The graph of the relation
From Figure 1, it is observed that the vertical line passing through 1 intersects more than one points so it cannot satisfy the vertical line test.
Therefore, the relation is not function.
Chapter 3 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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