Graphing y = tan(x - π/4)

Trigonometry · Axiom Academy

EXAMPLE Graphing y = tan(x - π/4) Learn to identify asymptotes and plot key points for horizontally shifted tangent functions. Excellent work! You've successfully graphed a horizontally shifted tangent function. Here's what we learned: Horizontal Shifts Affect Asymptotes: When tan(x) becomes tan(x - c), every feature shifts c units to the right, including all vertical asymptotes. Finding Asymptotes: Set the inside of the tangent equal to where the parent function has asymptotes (±π/2 + nπ), then solve for x. Key Point Strategy: Find where the argument equals 0 (for the center), then find intermediate points to sketch the S-curve shape. Period Remains Unchanged: Horizontal shifts don't change the period (π for tangent). The distance between consecutive asymptotes is still π. This same technique works for any transformation of the form tan(x - c). Always start by finding asymptotes, then locate key points to complete your sketch!

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