Question

The graph of the parabola x=y^2 is a function X → Y only when:

a. x is positive
b. x<-4
c. y is negative
d. x=4
e. y is non negative
f. x<4
g. x>-4
h. y is positive
i. nothing will make it into a function
j. x is negative
k. x>4

Answer 1

The graph of the parabola \( x = y^2 \) is a function \( X \rightarrow Y \) only when \( e. \) \( y \) is non-negative.

Step-by-step explanation:

To determine if the graph of the parabola \( x = y^2 \) represents a function, we need to examine the vertical line test. For a relation to be a function, each \( x \) value should correspond to a unique \( y \) value.

In the given equation \( x = y^2 \), every \( x \) value corresponds to two \( y \) values: one positive and one negative since \( y = \pm \sqrt{x} \). Therefore, to satisfy the criteria of a function, we consider only the non-negative values of \( y \).

Selecting option \( e. \) "y is non-negative" is the correct choice. This means that for each \( x \) value, there is only one non-negative \( y \) value, adhering to the definition of a function.

In summary, the graph of the parabola \( x = y^2 \) represents a function when \( y \) is non-negative. This ensures that each \( x \) value has a unique corresponding \( y \) value, fulfilling the criteria for a function.

The other options either include both positive and negative \( y \) values (violating the vertical line test) or impose additional conditions that do not guarantee a one-to-one correspondence between \( x \) and \( y \).