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Properties of the function f(x) = tan x. Domain: D = R \ (π/2 + kπ): k ∈ Z. Image: Imf = R. Zero: x_0 = kπ, k ∈ Z. Monotonicity: The function is monotonic on the intervals, strictly increasing on the intervals (-(π/2) + kπ, (π/2) + kπ), k ∈ Z. Injectivity: Function is not injective. Evennes or oddness: Even function. Period: Function is periodic. The period T = π.