Question

Which graph represents a function?

On a coordinate plane, a line with 2 angles crosses the x-axis at (negative .5, 0), the y-axis at (0, 1), turns at (1, 3), crosses the x-axis at (1, 0), turns at (1, negative 2), and crosses the x-axis at (2, 0).

On a coordinate plane, a curved line crosses the y-axis at (0, 1.5), the x-axis at (negative 2, 0), and the y-axis at (0, negative 1.5).

On a coordinate plane, a line enters the plane at point (negative 5, 4), makes a 90-degree turn at (negative 1, 0), and leaves the plane at point (negative 5, negative 4).

On a coordinate plane, a line with an s curve enters the plane at point (negative 3.75, 5), crosses the x-axis at (negative .75, 0), the y-axis at (0, 0), leaves x-axis at (.75, 0), and exits the plane at point (3.75, negative 5).

Answer 1

Use the vertical‑line test: a graph is a function iff no vertical line meets it more than once.

- Graph 1: fails — there are points (1,3), (1,0), (1,−2) so x=1 gives multiple y-values.
- Graph 2: fails — it crosses the y‑axis twice at (0,1.5) and (0,−1.5), so x=0 gives two y‑values.
- Graph 3: fails — it passes through (−5,4) and (−5,−4), so x=−5 gives two y‑values.
- Graph 4: passes — the S‑curve gives exactly one y for each x, so it represents a function.

Therefore the fourth graph is a function.