Determine as ass\u00edntotas do gr\u00e1fico de cada uma das seguintes fun\u00e7\u00f5es:<\/p>\n
\\[\\begin{array}{*{20}{c}}
\n{f\\left( x \\right) = \\frac{{2x – 1}}{{x + 3}}}&{\\text{e}}&{g\\left( x \\right) = \\frac{{2{x^2} – 7x + 3}}{{x – 3}}}
\n\\end{array}\\]<\/p>\n
\n\\[{f\\left( x \\right) = \\frac{{2x – 1}}{{x + 3}}}\\]<\/span><\/p>\n<\/blockquote>\n
\n
- ${D_f} = \\left\\{ {x \\in \\mathbb{R}:x + 3 \\ne 0} \\right\\} = \\mathbb{R}\\backslash \\left\\{ { – 3} \\right\\}$<\/li>\n<\/ul>\n
\\[f\\left( x \\right) = \\frac{{2x – 1}}{{x + 3}} = \\frac{{2\\left( {x + 3} \\right) – 7}}{{x + 3}} = 2 + \\frac{{ – 7}}{{x + 3}}\\]<\/p>\n
\u00a0\\[\\begin{array}{*{20}{c}}
\n{\\mathop {\\lim }\\limits_{x \\to\u00a0 – {3^ – }} f\\left( x \\right) =\u00a0 + \\infty }&{\\text{e}}&{\\mathop {\\lim }\\limits_{x \\to\u00a0 – {3^ + }} f\\left( x \\right) =\u00a0 – \\infty }
\n\\end{array}\\]<\/p>\nLogo, a reta de equa\u00e7\u00e3o $x =\u00a0 – 3$ \u00e9 uma ass\u00edntota vertical bilateral do gr\u00e1fico de $f$.<\/p>\n<\/p>\n
\\[\\begin{array}{*{20}{c}}
\n{\\mathop {\\lim }\\limits_{x \\to\u00a0 – \\infty } f\\left( x \\right) = {2^ + }}&{\\text{e}}&{\\mathop {\\lim }\\limits_{x \\to\u00a0 + \\infty } f\\left( x \\right) = {2^ – }}
\n\\end{array}\\]<\/p>\nLogo, a reta de equa\u00e7\u00e3o $y = 2$ \u00e9 uma ass\u00edntota horizontal do gr\u00e1fico de $f$, quando ${x \\to\u00a0 – \\infty }$ e quando ${x \\to\u00a0 + \\infty }$.<\/p>\n<\/p>\n
\n\u00a0\\[{g\\left( x \\right) = \\frac{{2{x^2} – 7x + 3}}{{x – 3}}}\\]<\/span><\/p>\n<\/blockquote>\n
\n
- ${D_g} = \\left\\{ {x \\in \\mathbb{R}:x – 3 \\ne 0} \\right\\} = \\mathbb{R}\\backslash \\left\\{ 3 \\right\\}$<\/li>\n<\/ul>\n
\\[g\\left( x \\right) = \\frac{{2{x^2} – 7x + 3}}{{x – 3}} = \\frac{{2\\left( {x – 3} \\right)\\left( {x – \\frac{1}{2}} \\right)}}{{x – 3}} = 2x – 1\\]<\/p>\n<\/p>\n
\\[\\begin{array}{*{20}{c}}
\n{\\mathop {\\lim }\\limits_{x \\to {3^ – }} g\\left( x \\right) = \\mathop {\\lim }\\limits_{x \\to {3^ – }} \\left( {2x – 1} \\right) = {5^ – }}&{\\text{e}}&{\\mathop {\\lim }\\limits_{x \\to {3^ + }} g\\left( x \\right) = \\mathop {\\lim }\\limits_{x \\to {3^ + }} \\left( {2x – 1} \\right) = {5^ + }}
\n\\end{array}\\]<\/p>\nLogo, o gr\u00e1fico da fun\u00e7\u00e3o $g$ n\u00e3o tem qualquer ass\u00edntota vertical.<\/p>\n<\/p>\n
\\[\\begin{array}{*{20}{c}}
\n{\\mathop {\\lim }\\limits_{x \\to\u00a0 – \\infty } g\\left( x \\right) = \\mathop {\\lim }\\limits_{x \\to\u00a0 – \\infty } \\left( {2x – 1} \\right) =\u00a0 – \\infty }&{\\text{e}}&{\\mathop {\\lim }\\limits_{x \\to\u00a0 + \\infty } g\\left( x \\right) = \\mathop {\\lim }\\limits_{x \\to\u00a0 + \\infty } \\left( {2x – 1} \\right) =\u00a0 + \\infty }
\n\\end{array}\\]<\/p>\nLogo, o gr\u00e1fico da fun\u00e7\u00e3o $g$ n\u00e3o admite qualquer ass\u00edntota horizontal.<\/p>\n<\/p>\n
![\"Representa\u00e7\u00e3o](\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-51-8.png\")
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