Graph exponential, logarithmic, and trigonometric functions with key features.
Graph tangent from center, zeros, and repeated asymptotes
Problem
Analyze \(y~=~\tan(x)\). 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.
For tangent, anchor the analysis at the center and compute its period before locating anything else. The nearest vertical asymptotes lie half a period on either side, and both the zeros and asymptotes repeat by whole periods. Plot familiar quarter-angle values inside one bounded interval, then draw an increasing branch that approaches but never crosses either asymptote.
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