Question

Which graph represents a function?

On a coordinate plane, a straight vertical line crosses the y-axis 0 times and the x-axis 1 time.

On a coordinate plane, a curved line crosses the y-axis 2 times and the x-axis 1 time.

On a coordinate plane, 2 curved lines are shown. Both lines touch the y-axis 1 time and the x-axis 1 time.

On a coordinate plane, a straight horizontal line crosses the y-axis 1 time and the x-axis 0 times.

Answer 1

Only the straight horizontal line (the fourth graph) represents a function.

Reason: Use the vertical line test — a graph is a function if any vertical line meets it at most once.
- The vertical line (1) fails: a vertical line has many y-values for one x.
- The curved line that crosses the y-axis twice (2) fails: x = 0 would give two y-values.
- The two curved lines (3) fail: both touch the y-axis, so x = 0 gives two different y-values.
- The horizontal line (4) passes: each x corresponds to exactly one y (y = constant).