Maths-
General
Easy
Question
What are the vertical and horizontal asymptotes of the graph of each function?
![fraction numerator x squared plus 5 x plus 4 over denominator 3 x squared minus 12 end fraction](data:image/png;base64,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)
Hint:
A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational function if, it can be represented as f(x) =
, where p(x) and q(x) are polynomials such that q(x) ≠ 0.
Rational functions are of the form y = f(x)y = fx , where f(x)fx is a rational expression .
- If both the polynomials have the same degree, divide the coefficients of the leading terms. This is your asymptote.
- If the degree of the numerator is less than the denominator, then the asymptote is located at y = 0 (which is the x-axis).
- If the degree of the numerator is greater than the denominator, then there is no horizontal asymptote.
The correct answer is: From the graph we can analyze that the vertical asymptote of the rational function is x= -2 and x = 2. and horizontal asymptote is y = (leading coefficient of numerator) / (leading coefficient of denominator) = 1/3
1.Find the asymptotes of the rational function, if any.
2.Draw the asymptotes as dotted lines.
3.Find the x -intercept (s) and y -intercept of the rational function, if any.
4.Find the values of y for several different values of x .
5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
3x2 -12= 0
3x2 = 12
x2 = 4
x = -2 or x = 2
The vertical asymptote of the rational function is x = −2 and x = 2
We will find more points on the function and graph the function.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKIAAAC8CAYAAAD7LnXwAAAPhklEQVR4nO2dv47bOB7HfwryBou9IgiChahnmCKYuEhh+QG2GHcpFgE0i2vHd8CUA9xpkO6wa2CxW2seIZ5iC1uYYou9F7CEQTBIcYs8A6+Y/DQ0TVGk/liU9fsAKixLMv3z1yJF/r6kxznnQBA986zvAhAEAAmRcAQSIuEEJETCCUiIhBOQEAknICESTkBCJJyAhEg4wXN5h+d5fZSDGAllA3l7QtQdPHY8z6PYNEB3k6OqmXACEiLhBCREwglIiIQTkBAJJ7AW4vn5OXieB2maFvtubm7A8zy4vr5utXBD5Pr6Wvl0OJvN4Pz8vIcSDQQuodi1RxiGnDG2c04URZXnDR2T2GRZxgGAJ0myt2+z2XRZPOfRxc/7ekCBSV9ZnufAGIM4juH+/h6Wy+Uo+tdM+xFnsxkAAHz8+BEAHu+Si8ViFDHSoY2fjWpFkiThALD37z9mbGODhGE4ihqjCl38at0RxWMZY7Ddbhv8T4aDaWywxkiSBE5OToAxBpvNBk5PTw9QSnfRxa/2UzM2vLMso4cUCd/3IQxDWK/X8McffwAAjF6EldjcPpHNZlNUyVgNjaEhbhIbBONC1fITuvjVqpqDIIAgCIrG+Gw2g+12e/RVtG3SA3bjULX8SKsPK2EYcgDgWZYV+7B7IgzDen+VgVAVGxmMFfGILhbKNDAdeBcU8X1/9F0TZURR1HcRBoG1EAkz0jSF1WoFWZb1XZRBQELsAGwbJkkCvu/3XJphQELsAGqm2KMUIvlWyqHYdAN5Viwgz0ozyLNCOA8JkXCC1oUYBAF4ngee50EQBG1ffjBgsjBuYiKxCUEQwM3NjfI98bpVybZlibqu0aoQPc+D6XQKnHPgnBdDgWMjTVOYz+ew2WyAcw6bzQbevHljLMbZbFba/xgEAURRVMT49va2VIx5nsNisaj9PQ6KzTCMjjiOd7K2OT++zGTT2KgSHaIoMhoCha85nqDI85TzHDl/SkARh1zFcuC1XEBXjtaEyBjjcRzXOncomMbGVEQyjDHOGFPaDTgvF7Pu8+I4HoQQW6uasyyDV69eFeaqsbYR8zwHAICXL1/u7MfX+L6KqgymPM+VIzWMMfj06dPOvvl8DkmSGJe7b1oRIgZ3Pp/DZDIp2i8AMDoxfv78ubNrm6bZnZ+fQxiGcHZ21llZ2qbVh5Uoina+/O3tLWRZVvr0R7RPmqawXC7h559/7rsoVrQqxMlksvPa931ltXHMvHjxorNrm9Qu7969G2SyhbUQsV9KbAei4AgoBPDw8LCzH183EYjv+8o2JrbP0zSFLMtgPp8Xvw9237g+AYK1EC8uLoo2IOe8aLdMp1NYr9c7x+Z5DlmWwevXr9sp7UBA45TIer2GMAwbXXcymcBqtdrZh32TJycncHp6uvPbcM4hjmMAeMwfuLi4aPT5nWLziK1D1eXAGDsq+4BpbGRDma3BrKz7Bssg9lHKr2WG0n3TmhDF83E7JhFyXs/Fh5sswjAMS+OjEyKWA7cqh+BQhNjIYD82KDbN6MRgTxBtQkIknICsApZQbLqBrAIWUBuxGWQVIJyHhEg4QatClIf/cOZUHWma7pyD27EmStik+SMm9guTuNv+NoekNSHi9LxZlu0M/1V94YeHB2CM7Q1NDSmFyRSbNH/xnCAIinOm0+meGD3P27kuAOzF3eSYXrHp/dahytDWpbEjURQNZv7AurHh3D7Nv+x92X5hct06n90Fuvi1dkfcbrelg+q6ZNHb29u99LFjRJX0gHMm4qyyMpjEoMvYOTs7q3ySNzmmbzp9WLm7uwMAfY5elmVweXnZyHo5BGzS/HWcn58DY0w78ee7d+8gDEOtgE2OOSg2t886t2JdtYvVg3iMy1MhN4kNY0wZC1PTWRRFRaJDWXVq4trr09mn+8zOhNhktlRdZkqf9ClEpCozh/OnP7juz2xyTNvo4tdJ1TybzRpNUvn27dujm4+7LROZ7/sQRRFcXl6WHnN6egphGMLV1VWjYw5JK1YBkSAIChE60/44IGXxqUrzt+G7776rPMYk9k79Pja3zyoYY7WSR2VcXRKiSWzqdKHgOfL7YtOlLPFVbAqYHHMIdPFrTYjYmLbtlwIpkxuDdsj+LVOaCBHPt0nzx2NU8cG2HbYZxevIv4XJMYegcyHiFy3bsGFd9g/HOylurtJG2cTvKYvQND4q8cgxr/rsPuKs+0yyClhAsWkGWQUI5yEhEk5AQiScgDwrllBsuoE8KxbQw0ozyLNCOA8JkXCC3j0reZ7v+VV00/sOnTqeldlspo2PvJSGnNcpTictb87M6GvT+61DNTRXNRsYjsiIaVDHPMQnj+2ajPXiUByiik8cx9Zpc33kferi16tnRbUkRtm1XKCJEOv6RkCReyj/ecMwtI4XGIxzt40ufr16Vi4uLkrzDu/v79sqmhPU8ayYslqtrCZDxZljXZpnu3fPigzOMmuSczck6npWoiiC+XxevEYRff/998V1AR49KKbt7MViUcwk6ww2t886t2Lb27/cJnKJJuVqYhXAdiEA7DVlxIV95ONVVX6fbXBd/JzyrGBQdX6MPulDiPIDn2mMdJ/Xlx/o4EJEEdr861T/bNdoEpuyrHOdEMvyE6MoUj7kycfIgjMxXnWJLn5OeFaur69hPp9DHMduz3xvQJueFWw7ynGs237Gh6KTk5Na53eKjWqrsPWscP7UZnG1OhZpEps2PSvi3c6mC8zkTtoluvj16lnBH8Ll6likiRDxfFvPCq5YishtRJ0fRaZvv3jnQqzrWRFnHZC3YzPYi9fAzdSzIsdJNRoivl921zu0a09GFz/yrFhAsWkGeVYI5yEhEk5AVgFLKDbdsCdEagMRfUBVM+EEJETCCUiIhBM8//XXX3d2/PDDDz0VhRgzz0XhyaIkiENBVTPhBCREwglIiIQTPPvfX3/1XQaCgGeLf/wT/vzzv32Xgxg5z758+QL/+emnvstBjJxn33zzDfz9xx/7Lgcxcp7H//4X/O3bb/suBzFynpEICReg7hvCCUiIhBOQEAkn2Mu+IYg+UNpJCaIryqwotLyFBeRrbgYtb0E4DwmRcAISIuEEJETCCUiIhBNYCxFXMcJVjQCeVj7CGe/HDM4YKzObzYxXmholNnPYIWEY7szBBz0sHtMHJrFRzVON+w65ypOL6OJXa37EPM+BMQZxHMP9/T0sl8tR9K+Z9iPiGoQfP34EgMe75GKxGEWMdGjjZ6NaEZzdFAYy/3Ub2MYGKVtRYGzo4tdoxljP84AxVrqM2bFhGhusMZIkgZOTE2CMwWazKZY8GyudzBiLDe8sy+ghRcL3fQjDENbrdbGkxNhFWInN7RPB1QCSJOlludW+MIkNgnGhavkJXfxqVc1BEEAQBEVjfDabwXa7Pfoq2jbpAbtxqFp+pNWHFdXyZtg94eKSFG1SFRuZOusRHjO6WCjTwHTgXVDE9/3Rd02UEUVR30UYBNZCJMxI07RYk5CohoTYAdg2TJLEeGHMsUNC7ABqpthD66xYQrHpBvKsWECelWaQZ4VwHhIi4QTWQkzTFDzPK93EhNkxg8nCtnEJgqA4JwiCvfcxMVnedMcMIiHXpve7qtf82MdUTWODY/E4/i6/1l1fjKGcgIz74jguvYZq9XpXfhtd/FoRourLHyOm31GV6BBFkXYINI7jPdGpMrurBA2K/FA5P7IvOhWiKjX+WDGNTR0xMMa0dzrOn+6stuBni/kBfaAre+OHlQ8fPgBjDM7Ozppe6ijI8xwAAF6+fLmzH1/j+zJZlsGrV6922ndyG/Hh4QEYYzvtP1U7Uma9XgMAOD3K00iIeZ7DcrmE9+/ft1WewfP582frc1Cc8/kcJpMJ8MeaCgBgR2jr9RqyLIPNZlMcgyl5umsvl0uI49i6XAfF5vYpE8exE7f8Q2ESm7IHE9yvihU2b+R2pUmzp+oYxthe27MvdPFrNNb8+++/QxiGTt/yD82LFy9qnzuZTHZe+74PjDH49OlT6Tm6Y4IggCzLBjEa1KhqXq1W8Pbt27bKchTgn/Lh4WFnP75W/WlRTG3ied5gRAjQQIjYQfv69evWCnMsoHFKZL1eQxiGpedMp9O9c/I8hyzLihirZouQjwF4clcORYQA0NzXPJb2Ief2scF2oonBTNXWY4zt9D3idXTHuGxP0JWrthDxQWVM2HxfcQIClQjDMFR2cIvnqN7Hhx7cxAcc+T1569tpqYtfI4P92KDYNKMTgz1BtAkJkXACsgpYQrHpBrIKWEBtxGaQVYBwHhIi4QSNpqUT05HK0pvGDlorTMjzfCemOPOsjM5OoLNxOD19oE2nIyJnZI9llMUkNiI4WmJ6Hkgd1PKoieoYlZ1AxuSYQ6CLQy0hgiLtyCTDeOjYCFEeWTE9XrUP/+CmdgLVNfoeVeG8gzQwTk+OWtI0hfl8XiSjLhaLVq77yy+/7CUhV83Ednl5CVEUuT8/o41qyxhLgmyT2JheX1c1w9eaCJtGAKCtcl1rMuni0EiIY1tZoGshcv4oPoyp2NQR25ty9k2ZGFVtzD7pTIgijDEnvLNd0qUQxXnJETGly9ZOoLpe3+ji0Fo/4tXVFSyXS+rGqcnV1RWEYbjjhhQXDEJM7QR3d3cAAINxV7YmRNk+Sdix3W6VNgK0ENjaCdBPNBSshYidrjc3Nzv78R9IRqp6BEGgrE3Q7wxgZidABucnsqnHETkdHdsj1I+4j20bUYyhHGcTO0HZcS6gi0PthxWxC8HFL90FbQpRZRUQn4xB0zUjHqOzE7jQiS2iix9ZBSyg2DSDrAKE85AQCScgIRJOQJ4VSyg23UCeFQvoYaUZ5FkhnIeESDhBbSGqPBGDWEbhQNRZ3sLEs1K1vMWoPCs4AuBKwuWhMIkN5+0tb6Eavqta3kLF0XpWkiRx4osdGlMh1lnewsSzgmWwGbobimelVtW8Xq9hOp02vx0fKavVai9vcDKZwGq1anRdrN5t/CdH7VnBWz0Ig+/HnnnDuV2zxWYyd/H6uqoZayIx7sfiWal1R8R/Nv+6xEKWZbBYLNxuDB+IOstbIJxzuL29LR4u3r9/X2RpA9gvb3F5eTmcyfZtVKtjDDPImny/OstbiO+XeVbKIM+KBGYIj92zUnd5C1PPigx5VggldZa3AKj2rNgyGs+K3EF7d3cHjLFhtEc6ps7yFiaeFdPlLQBG7llxqT3SBSax4bze8hYmnhWT5S04H7lnxYUO064xjQ3n9Za3MPGs6Ja3kI9x7TfRxY88KxZQbJpBnhXCeUiIhBOQVcASik037AmR2kBEl/z222/K/f8HWhDyQT/V1VEAAAAASUVORK5CYII=)
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)
From the graph we can analyze that the vertical asymptote of the rational function is x= -2 and x = 2. and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) =![1 third](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAKNJREFUeNpjYMAP1IC4FogvMFAIFgNxGhD/Z6ASGDVo1KBBYdB/LHgUDCbwn0w8CgYLcATibUD8DYh/APEtIJ4AxMKkGrQfiIOAmA1JzACId1DLpZ+oYYgSEN+gxABxIE6EhpMXNbJMAaVeEgTiACA+CcT21AgjHqhhVAE/qGGIHjTASQIHgTgUiFmAmAma0u8DcTypBtkC8RaoV35AU7oPPg0ArQs4erRAu/EAAABidEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xPC9tbj48bW4+MzwvbW4+PC9tZnJhYz48L21hdGg+q+QgMwAAAABJRU5ErkJggg==)
Related Questions to study
Maths-
The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is parallel to the north path.
The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is parallel to the north path.
Maths-General
Maths-
Write recursive formula and explicit formula. 12,19,26,33,40,...
Write recursive formula and explicit formula. 12,19,26,33,40,...
Maths-General
Maths-
What are the vertical and horizontal asymptotes of the graph of each function?
![G left parenthesis x right parenthesis equals fraction numerator 2 x squared plus x minus 9 over denominator x squared minus 2 x minus 8 end fraction](data:image/png;base64,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)
What are the vertical and horizontal asymptotes of the graph of each function?
![G left parenthesis x right parenthesis equals fraction numerator 2 x squared plus x minus 9 over denominator x squared minus 2 x minus 8 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Are graphs of the equations parallel, perpendicular or neither?
![y equals negative 5 x space straight & space 25 x plus 5 y equals 1](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALEAAAASCAYAAAAUoT+FAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAARqpSybAAAArpJREFUeNrtWU1kHVEYfZ6Iqm4qniyyKFFVERWii+qiSkREPFEiIiqidFlPNl1VRITq4i0quqkuqiJUVVRFqIiIiFBRTxZVqssuQhddRMQjPZ+ecD3zc2c68747eg9HZib3ju/nzL3f/V6pVDycRTBr9ICb4Cn4BRywmHMbfAf+NuZNK/vhanyT4Br4hPEsPNoZzF3wLq+Hwa8Wc7bBKfAS7/v4nilFP1yNbxK8AR86bJ+zQZaVtMxr+Xuc8j1XwIayWM4KLuJY+16BkwHPa+BSgUX8AHwa8HyR/4vDFjjKaykJXvyD3SeKfuQhYi3NhNo3Az5reXYR/AZ2Jayb8q6fkr77AOw27mfBZcu5Q+APlgjPwY6UNt9iSaHlRx4i1tJM6DhZbd62PJtnIe3idnLKg9M6OGfUn0EYAeuGKDcTJOkneETBpMUFcJ8HPg0/0ojYxi4tzYT6IV/OoXFfAb8zARqnYJsvU1bFQQZNDlzXI8Z+Au/wZNtlYdsEuAFeZhI3YkqDMMj8NR4K2+1H3vHV0Ezsx2geWuqsbfIKUNYY5pYfhhpXlxsJtu6KkUxJzoCxZTYs3tFLAV9V9COrA1uYXRqaiRy3w8D3MmnlgnUtwlbH875tPaDNZdOVEFRZEpyXGfMx82XVeknBa/qRZdfhxBHNRPrxmslaAe8XTMD9DGLQaviBYpK67rNlORH0A4XUf4/YsYh6RzfHdjjgR1YiDrNLQzORftTYNmk4Ltj3PO2XyREG+F7LuAoPJmayx0p/m+ZxkMT8YgupTEE+BpusS6PwMaaubacfaURsa5eWZiL9GOeAquMinmAbp0mhyap3s2VMJ5PREzB/lYmJwyhXvCa3UukGLDBGCylrPw0/8oivhmasamgxZK/k4WEP5zSzzm3Ew6OQmulnLefh4TXj4eHh4eHh8b/hDytmHtEl4xdfAAABHXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT55PC9taT48bW8+PTwvbW8+PG1vPiYjeDIyMTI7PC9tbz48bW4+NTwvbW4+PG1pPng8L21pPjxtbz4mI3hBMDs8L21vPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj4mYW1wOzwvbWk+PG1vPiYjeEEwOzwvbW8+PG1uPjI1PC9tbj48bWk+eDwvbWk+PG1vPis8L21vPjxtbj41PC9tbj48bWk+eTwvbWk+PG1vPj08L21vPjxtbj4xPC9tbj48bXNwYWNlIGxpbmVicmVhaz0ibmV3bGluZSIvPjwvbWF0aD4qPnh3AAAAAElFTkSuQmCC)
Are graphs of the equations parallel, perpendicular or neither?
![y equals negative 5 x space straight & space 25 x plus 5 y equals 1](data:image/png;base64,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)
Maths-General
Maths-
Tell whether the given sequence is an arithmetic sequence. 93,86,79,72,66,...
Tell whether the given sequence is an arithmetic sequence. 93,86,79,72,66,...
Maths-General
Maths-
Are graphs of the equations parallel, perpendicular or neither?
![y equals 2 x plus 6 space straight & space y equals 1 half x plus 3](data:image/png;base64,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)
Are graphs of the equations parallel, perpendicular or neither?
![y equals 2 x plus 6 space straight & space y equals 1 half x plus 3](data:image/png;base64,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)
Maths-General
Maths-
Tell whether the given sequence is an arithmetic sequence. 37,3,31,29,26,23,...
Tell whether the given sequence is an arithmetic sequence. 37,3,31,29,26,23,...
Maths-General
Maths-
What are the horizontal asymptotes for the graph
![f left parenthesis x right parenthesis equals fraction numerator 3 x minus 2 over denominator x squared plus 7 x plus 12 end fraction](data:image/png;base64,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)
What are the horizontal asymptotes for the graph
![f left parenthesis x right parenthesis equals fraction numerator 3 x minus 2 over denominator x squared plus 7 x plus 12 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Tell whether the given sequence is an arithmetic sequence. 3,6,9,15,18,...
Tell whether the given sequence is an arithmetic sequence. 3,6,9,15,18,...
Maths-General
Maths-
Tell whether the given sequence is an arithmetic sequence. 3,6,9,12,15,18,...
Tell whether the given sequence is an arithmetic sequence. 3,6,9,12,15,18,...
Maths-General
Maths-
Tell whether the given sequence is an arithmetic sequence. 1,-2,3,-4,5,...
Tell whether the given sequence is an arithmetic sequence. 1,-2,3,-4,5,...
Maths-General
Maths-
Tell whether the given sequence is an arithmetic sequence. 77,64,51,38,25,...
Tell whether the given sequence is an arithmetic sequence. 77,64,51,38,25,...
Maths-General
Maths-
Tell whether the given sequence is an arithmetic sequence. 1,15,29,43,57,....
Tell whether the given sequence is an arithmetic sequence. 1,15,29,43,57,....
Maths-General
Maths-
Write a recursive formula for the given sequence. 47, 39, 31, 23, 15, ....
Write a recursive formula for the given sequence. 47, 39, 31, 23, 15, ....
Maths-General
Maths-
Write a recursive formula for the given sequence. 81,85,89,93,97,....
Write a recursive formula for the given sequence. 81,85,89,93,97,....
Maths-General