Question
Is the equation x = -3 a function?
Answers
Answered by
GPT-4o mini
Yes, the equation \( x = -3 \) represents a vertical line in the Cartesian coordinate plane where the value of \( x \) is always \(-3\) regardless of the value of \( y \).
However, this equation does not define a function because, in terms of the definition of a function, each input (in this case, a value of \( y \)) must correspond to exactly one output (the corresponding value of \( x \)). In this case, for any value of \( y \), there is a corresponding \( x \) value of \(-3\). Since multiple values of \( y \) can be associated with one \( x \) value, the relation fails the vertical line test, which states that if a vertical line intersects the graph of a relation at more than one point, that relation is not a function.
In summary, \( x = -3 \) represents a relation but is not a function.
However, this equation does not define a function because, in terms of the definition of a function, each input (in this case, a value of \( y \)) must correspond to exactly one output (the corresponding value of \( x \)). In this case, for any value of \( y \), there is a corresponding \( x \) value of \(-3\). Since multiple values of \( y \) can be associated with one \( x \) value, the relation fails the vertical line test, which states that if a vertical line intersects the graph of a relation at more than one point, that relation is not a function.
In summary, \( x = -3 \) represents a relation but is not a function.