Which statement best describes the period of ?

Question

BlackTom AI · Accepted Answer

Let's break down what is meant by the period of a function like f(x) = tan(x).
Option a: π/2. This would imply the function repeats every π/2 units. However, tan(x) has vertical asymptotes at x = π/2 + kπ, and its basic repeating pattern occurs over an interval of length π, not π/2. So π/2 cannot be the fundamental period.
Option b: π. This is the standard period of the tangent function. The tangent function satisfies tan(x + π) = tan(x) for all x where both sides are defined, meaning its pattern repeats every π along the x-axis. This matches the graph’s repeating cycle between consecutive asymptotes, which are π apart.
Option c: ∞. Saying the period is infinite would mean the function never repeats, which is false for tan(x). It has a clear, regular repetition every π.
Option d: 2π. While 2π is a multiple of the fundamental period, the smallest positive amount that repeats tan(x) is π, not 2π. So 2π is not the fundamental period, though the function does repeat again after 2π as well.
In summary, the period concept asks for the smallest positive length T such that tan(x + T) = tan(x) wherever both sides are defined. The only option that matches this property as the smallest such length is π.

MHF4U - Advanced Functions 12 (2025-26) - A

Which statement best describes the period of ?

View Explanation

Log in for full answers

Similar Questions

Which equation best describes this function?

An oscillating voltage compressed horizontally is modeled by:Determine the domain, range, and period of the function if 0 < x < 2π

Given the function: What are the amplitude, period, and phase shift?

If and is in Quadrant II, what is ?

Using the relationship between the sine function and its reciprocal, which of the following describes the restrictions on the domain of when 0 < x < 2π

More Practical Tools for International Students

Exam Browser Assistant

Stylized Writing Assistant

Plagiarism Checker Assistant

Citation Assistant

In-Class Translation Assistant

Class Notes Assistant

Quiz Search Assistant

Past Exam Questions by School

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler