Question

which graph represents a function?

Explanation:

Step1: Recall function test rule

Use the Vertical Line Test: A graph represents a function if no vertical line intersects the graph more than once.

Step2: Test first graph

Any vertical line will cross this graph at most once. It satisfies the test.

Step3: Test second graph

A vertical line through the circle (e.g., $x=0$) crosses twice. Fails the test.

Step4: Test third graph

A vertical line (e.g., $x=-1$) crosses the left-opening curve twice. Fails the test.

Step5: Test fourth graph

The vertical line $x=1$ crosses the vertical segment twice. Fails the test.

Answer:

A. The first graph (the curved line passing through the origin with one branch in the first quadrant and one in the third quadrant)