Question

1. which of the following graphs does not represent a function?

a. a cubic curve.
b. a circle.
c. a parabola opening upwards.
d. a straight line.

Explanation:

To determine which graph does not represent a function, we use the vertical line test: a graph represents a function if no vertical line intersects it more than once.

• A cubic curve: Passes the vertical line test (each \(x\) has one \(y\)).
• A circle: Fails the vertical line test (a vertical line can intersect a circle at two points, e.g., \(x = h\) intersects \( (x - h)^2+(y - k)^2 = r^2\) at two \(y\)-values).
• A parabola opening upwards: Passes the vertical line test (each \(x\) has one \(y\)).
• A straight line (non - vertical): Passes the vertical line test (each \(x\) has one \(y\)).

So the circle does not represent a function.

Answer:

b. A circle.