Problem

Use the parent \(\text{secant}\) graph and \(\sec(x)~=~1/\cos(x)\) to state its real domain, excluded radian inputs using integer \(k\), the denominator reason, and its range as a separate set.

Exact secant graph with faint cosine source, repeated excluded inputs, and achieved branch vertices but no domain or range formulas.

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Its domain is all real numbers except pi/2 + k*pi, for integer k; excluded inputs are pi/2 + k*pi, for integer k; the reason is that cos(x) = 0 in sec(x) = 1/cos(x); and its range is (-infinity, -1] union [1, infinity).

Its domain is [-1, 1]; excluded inputs are pi/2 + k*pi, for integer k; the reason is that cos(x)=0 in the denominator; and its range is all real numbers.

Its domain is all real numbers; excluded inputs are none; the reason is that sec(x) is treated as having no zero denominator; and its range is (-infinity, -1] union [1, infinity).

Its domain is all real numbers except 90 + 180k, for integer k; excluded inputs are 90 + 180k without degree units; the reason is that cos(x)=0; and its range is (-infinity, -1] union [1, infinity).

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Use the parent \(\text{secant}\) graph and \(\sec(x)~=~1/\cos(x)\) to state its real domain, excluded radian inputs using integer \(k\), the denominator reason, and its range as a separate set.

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