To find:the domain of the given relation and draw the function also whether the relation is a function or not.
Answer to Problem 20WE
The domain of the relation is set of all integer and the relation is not a function.
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
Note that, the modulus of x defines as
By using the definition of the modulus, the values of
If the value of
That is, the values of x are all integer when
Therefore, the domain of the relation is set of all integer.
If the value of
That is, the values of y are all integer when
Therefore, the range of the relation is a set of all integer.
Suppose that
That is, the ordered pairs are
Suppose that
That is, the ordered pairs are
A function is relation in which different ordered pairs has different first coordinates.
Here, the different ordered pairs
Therefore, the relation is not a function.
Graph:
The graph of the relation
From Figure 1, it is observed that the vertical line passing through 0 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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