Question

Which graph is a function of x?
On a coordinate plane, a vertical line is at x = negative 3.

On a coordinate plane, a v-shaped graph opens up.

On a coordinate plane, a parabola opens to the right.

On a coordinate plane, one curve opens to the left and another curve opens to the right.

Answer 1

The v-shaped graph that opens up.

Reason: A graph is a function y = f(x) if every vertical line meets it at most once (vertical line test).
- The vertical line x = −3 fails the test (it meets the graph at infinitely many y).
- The V-shape opening up passes the test (each x has exactly one y).
- A parabola opening to the right (e.g. x = y^2) fails (many x correspond to two y-values).
- Two opposite-opening curves also fail (vertical lines hit them more than once).