AP® Precalculus – The Tangent Function – Drill 1

About This Drill

AP® Precalculus – The Tangent Function – Drill 1 is a Math practice drill covering The Tangent Function. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Master the distinctive properties of the tangent function on the AP® Precalculus exam: its period of π (not 2π), vertical asymptotes at odd multiples of π/2, and behavior on restricted intervals. Practice identifying asymptotes, finding periods of transformed tangent functions, and applying domain reasoning to real-world models.

Questions in This Drill

1. What is the period of the function \( f(x) = \tan(x) \)?
2. Which of the following correctly describes the vertical asymptotes of \( f(x) = \tan(x) \)?
3. What is the period of \( g(x) = \tan(3x) \)?
4. On which of the following intervals is \( f(x) = \tan(x) \) continuous and increasing?
5. A surveyor stands at point A and measures the angle of elevation θ to the top of a building. The horizontal distance from the surveyor to the base of the building is 80 feet. The height of the building is given by \( h = 80\tan(\theta) \). For which value of θ is this model undefined?