Problem

Analyze \(y~=~\tan(2x)\). State \(B\), \(h\), \(D\), period, shifts, and center; give the repeating zero and asymptote families and nearest asymptote pair; list \(\text{three}~\text{central}\text{-}\text{branch}~\text{anchors}\); and state the domain, range, and monotonic behavior.

Prompt coordinate grid scaled for the stated tangent equation; the branch, asymptotes, center, and anchors are withheld.

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Parameters: B = 2, h = 0, D = 0; period π/2; no shifts; center (0, 0).
Families: zeros x = kπ/2; asymptotes x = π/4 + kπ/2; nearest pair −π/4 and π/4.
Branch: anchors (−π/8, −1), (0, 0), (π/8, 1); domain all real x except the asymptote family; range all real numbers; increasing.

Parameters: B = 2, h = 0, D = 0; period 2; no shifts; center (0, 0).
Families: zeros x = kπ/2; asymptotes x = π/4 + kπ/2; nearest pair −π/4 and π/4.
Branch: anchors (−π/8, −1), (0, 0), (π/8, 1); domain all real x except the asymptote family; range all real numbers; increasing.

Parameters: B = 2, h = 0, D = 0; period π/2; no shifts; center (0, 0).
Families: zeros x = kπ/2; only asymptote x = π/4, with no repeating family or left partner.
Branch: anchors (−π/8, −1), (0, 0), (π/8, 1); domain all real x except π/4; range all real numbers; increasing.

Parameters: B = 2, h = 0, D = 0; period π/2; no shifts; center (0, 0).
Families: zeros x = π/4 + kπ/2; asymptotes x = kπ/2; nearest pair −π/2 and 0.
Branch: anchors (−π/8, −1), (0, 0), (π/8, 1); domain all real x except x = kπ/2; range all real numbers; increasing.

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Analyze \(y~=~\tan(2x)\). State \(B\), \(h\), \(D\), period, shifts, and center; give the repeating zero and asymptote families and nearest asymptote pair; list \(\text{three}~\text{central}\text{-}\text{branch}~\text{anchors}\); and state the domain, range, and monotonic behavior.

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