Question

Does the equation (y² = x² + 5x + 4) represent a function?

a) Yes, the equation is a function because there is only a single term that contains the variable y.
b) No, the equation is not a function because there are multiple terms that contain the variable x.
c) No, the equation is not a function because some values of x result in more than one value of y, such as (x=0) resulting in (y=2) or (y=-2).
d) No, the equation is not a function because some values of y result in more than one value of x, such as (y=0) resulting in (x=-1) or (x=-4).

Answer 1

The equation y² = x² + 5x + 4 is not a function because, for any given x value, there can be two corresponding y values, which does not fit the definition of a function.

Step-by-step explanation:

The equation in question is y² = x² + 5x + 4. To determine if this equation represents a function, we use the definition of a function, which states that every value of the independent variable (x) should correspond to exactly one value of the dependent variable (y). According to the equation given, for any value of x, there can be two values for y (one positive and one negative) since we are dealing with y². Hence, multiple values of y can correspond to a single value of x. This contradicts the definition of a function. An example is x=0 resulting in y=2 or y=-2. So, the correct response is option c) No, the equation is not a function because some values of x result in more than one value of y.