Problem

Compare the domains, discontinuities, asymptotes, left- and right-end signs, and growth orders of \(f(x)~=~x^3\) and \(g(x)~=~x~+~1~+~4/(x~-~2)\).

Cubic and rational graphs with a vertical boundary at x 2 and dashed line y equals x plus 1.

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Analysis: f(x) = x³ is continuous with cubic growth from −∞ to ∞. g excludes x = 2, has slant asymptote x = 2 and vertical asymptote y = x + 1; both have the same end-limit signs, but their growth orders differ.

Analysis: f(x) = x³ is continuous with cubic growth from −∞ to ∞. g excludes x = 2, has vertical asymptote x = 2 and slant asymptote y = x + 1; both have the same end-limit signs, but their growth orders differ.

Analysis: f(x) = x³ excludes x = 2 and has vertical asymptote x = 2 from −∞ to ∞. g excludes x = 2, has vertical asymptote x = 2 and slant asymptote y = x + 1; both have the same end-limit signs, but their growth orders differ.

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Compare the domains, discontinuities, asymptotes, left- and right-end signs, and growth orders of \(f(x)~=~x^3\) and \(g(x)~=~x~+~1~+~4/(x~-~2)\).

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