If the x-value has multiple y-values that it maps to, this indicates that the relationship is not a function. In a function, each input (x-value) must correspond to exactly one output (y-value). If one x-value corresponds to multiple y-values, then the relation is classified as a relation but not a function.
Given the domain and range you specified:
- Domain: \((- \infty, \infty)\) indicates that the input values can take any real number.
- Range: \((- \infty, \infty)\) indicates that the output values can also take any real number.
This scenario could occur in relations like circles or other shapes where multiple y-values correspond to the same x-value (for example, in the equation of a circle, such as \(x^2 + y^2 = r^2\), where each x-value in the domain can correspond to two different y-values for most cases).
In summary, if an x-value maps to multiple y-values, you do not have a function, even though the domain and range indicate that both inputs and outputs can be any real number.