Use the graph to determine the domain and range of the relation, and whether the relation is a function.

 The correct option is

(c) Domain: {x | -8 ≤ x ≤ 8}; 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 : {x | -8 ≤ x ≤ 8} and Range: all real numbers.

Thus, Domain: {x | -8 ≤ x ≤ 8}; Range: all real numbers; No. it is not a function.

Option (C) is CORRECT.

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