Do the vertical asymptotes of y = tan x repeat every π units?

Study for the NBCT Mathematics AYA Component 1 exam. Utilize flashcards and multiple-choice questions with detailed explanations for each question. Prepare efficiently for success in your teaching certification journey!

Multiple Choice

Do the vertical asymptotes of y = tan x repeat every π units?

Explanation:
Vertical asymptotes for tan x occur where cos x = 0, which happens at x = π/2 + kπ for integers k. The distance between consecutive asymptotes is π, so the pattern repeats every π units. This fits with tan x having period π, meaning the graph—and where it blows up to infinity—repeats every π along the x-axis. It isn’t about x-dependent shifting; those fixed lines define the repeating structure. So the vertical asymptotes do repeat every π units.

Vertical asymptotes for tan x occur where cos x = 0, which happens at x = π/2 + kπ for integers k. The distance between consecutive asymptotes is π, so the pattern repeats every π units. This fits with tan x having period π, meaning the graph—and where it blows up to infinity—repeats every π along the x-axis. It isn’t about x-dependent shifting; those fixed lines define the repeating structure. So the vertical asymptotes do repeat every π units.

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