Question

which of the following graphs does not represent a function?
a. a cubic curve.
b. a straight line.
c. a circle.
d. a parabola opening upwards.

Explanation:

To determine if a graph represents a function, we use the vertical line test: a graph is a function if no vertical line intersects it more than once.

• A cubic curve (e.g., \(y = x^3\)) passes the vertical line test.
• A straight line (e.g., \(y = mx + b\)) passes the vertical line test (unless it's vertical, but a general straight line isn't vertical).
• A circle (equation \(x^2 + y^2 = r^2\)) fails the vertical line test: for some \(x\)-values, a vertical line will intersect the circle at two points (e.g., \(x = 0\) intersects \(y = r\) and \(y = -r\) for a circle centered at the origin).
• A parabola opening upwards (e.g., \(y = x^2\)) passes the vertical line test.

So the circle does not represent a function.

Answer:

c. A circle.