Answer: The correct option is
(c) Domain: x ; Range: all real numbers; No. it is not a function.
Step-by-step explanation: We are given to use the graph to determine the domain and range of the relation, and to check whether the relation is a function or not.
Function: A relation y = f(x) is said to be a function if each value of the independent variable x results in exactly one value of the dependent variable y.
From the graph, we notice that
for x = 4, there are two values of y, i.e., y = 4 and 10. So, (4, 2) and (4, 10) lies on the graph of the given relation.
Hence, the given relation is not a function.
Domain and range: The set of all values of the independent variable x is called the domain and the set of corresponding values of the dependent variable is called the range.
From the graph, we see that the values of independent variable x varies from -8 to 8 and the values of dependent variable y varies from -∞ to ∞.
Therefore,
Domain : -8 ≤ x ≤ 8 and Range: all real numbers.
Thus, Domain: -8 ≤ x ≤ 8; Range: all real numbers; No. it is not a function.
Option (C) is CORRECT.