Which of the following graphs represent a function?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) →
A function of x gives exactly one value of y for each x. On a graph this is the vertical line test: the graph is a function if no vertical line meets it at more than one point.
In Option (3) the curve opens upwards from the origin. Each vertical line meets it at one point at most, so it represents a function.
Why the other options are incorrect
Option (1) — Incorrect. It is a circle; a vertical line through any point inside it, such as the y-axis, meets it twice, once above and once below the x-axis.
Option (2) — Incorrect. The curve opens to the right; a vertical line just to the right of the y-axis meets it twice, once above and once below the x-axis.
Option (4) — Incorrect. The curve opens to the left; a vertical line just to the left of the y-axis meets it twice, once above and once below the x-axis.