Consider y = −4 tan(0.5(x + π)) + 2. Which statement is true?

Period is 2π; midline y = 2; reflected across x-axis

Period is π; midline y = −2; reflected across y-axis

Period is π; midline y = 2; reflected across x-axis

Period is 2π; midline y = −2; no reflection

Given y = 5 tan(3(x − π/6)) − 1. What are asymptotes in 0 < x < π?

x = π/6 + kπ/3 for integers k with result in (0, π)

Which statement about y = tan(bx) is true?

Increasing b compresses the graph horizontally and decreases the period.

Increasing b stretches the graph horizontally.

Increasing b increases the vertical stretch.

Increasing b shifts the midline.

The graph of y = −tan(x − π/2) is equivalent to which transformation of y = tan(x)?

Reflect across x-axis and shift right by π/2

Reflect across y-axis and shift right by π/2

Shift left by π/2 and reflect across y-axis

A tangent graph has midline y = −2, inflection at (1, −2), asymptotes at x = 0 and x = 2. Which equation?

y = −2 tan(π/2 (x − 1)) − 2

Which transformation maps y = tan(x) to y = −2 tan(x − π/4)?

Vertical stretch by factor 2, reflection across x-axis, and right shift by π/4

Horizontal stretch by factor 2, reflection across y-axis, and left shift by π/4

Vertical stretch by factor 2, reflection across y-axis, and right shift by π/4

Horizontal compression by factor 2, reflection across x-axis, and left shift by π/4

Tangent Graphs: Period, Asymptotes, Shifts & Midlines Study Guide

Reviewed by Cierra Henderson

Cierra Henderson, MBA |

K-12 Expert

Review Board Member

Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.

, MBA

By Thames

Thames

Community Contributor

Quizzes Created: 11371 | Total Attempts: 9,893,164

| Attempts: 11 | Questions: 20 | Updated: Jan 22, 2026