Question

in which choice is y a function of x?
a.

x	3	4	5	3	6
y	5	7	9	-1	11

b. {(-3, 6), (4, 5), (4, -2), (3, 8)}
c.
graph of a parabola opening downward with vertex at (0,0)
d.
graph of a curve where for some x-values there are two y-values

Explanation:

A relation is a function if each input (x-value) has exactly one output (y-value).

• For option A: The x-value 3 maps to both 5 and -1, so it is not a function.
• For option B: The x-value 4 maps to both 5 and -2, so it is not a function.
• For option C: Using the vertical line test, any vertical line drawn on the graph intersects the curve at most once, meaning each x has only one y-value.
• For option D: Using the vertical line test, some vertical lines intersect the curve twice, meaning one x maps to two y-values, so it is not a function.

Answer:

C. (The downward-opening parabola graph)