Which statement describes a vertical asymptote?

• A. Horizontal lines that the graph never touches
• B. A point where the function is continuous
• C. Invisible lines that go up and down that the graph never touches
• D. The intercept on the y-axis

Answer: (C)

Vertical asymptotes describe lines the graph approaches where the function becomes unbounded as x gets close to a certain value. As x nears that value, the y-values shoot off to positive or negative infinity, so the graph climbs toward a vertical line without ever meeting it. A classic example is 1/x, which has a vertical asymptote at x = 0: as x → 0 from the left, y → −∞, and as x → 0 from the right, y → ∞. The statement captures this idea by describing an invisible vertical line that the graph approaches and along which the values blow up, never actually touching that line. Horizontal lines the graph never touches describe horizontal asymptotes, the y-intercept is just a single point where the graph crosses the y-axis, and a point of continuity isn’t about unbounded behavior.