Question

Lorraine writes the equation: x ^2+y−15=0. What does this equation represent in terms of relation and function?

A. A relation and a function
B. A relation but not a function
C. A function but not a relation
D. Neither a relation nor a function

Answer 1

The equation x ^2+y−15=0 represents a relation but not a function because each input x can produce two values of y, which violates the definition of a function where each input must correspond to only one output.

Step-by-step explanation:

Lorraine writes the equation: x ^2+y−15=0. This equation represents a relation, which can be a set of ordered pairs (x, y), but does not represent a function. A function is a special type of relation where each input has exactly one output. However, for any given value of x, this equation might have two possible values of y (one positive and one negative) because of the x2 term. Thus, not every x corresponds to a unique y value. In conclusion, the given equation is a relation but not a function, so the correct answer is B. A relation but not a function.