Question
What is the horizontal asymptote of the rational function
![straight F left parenthesis straight x right parenthesis equals fraction numerator a x squared plus b x plus c over denominator d x squared plus e x plus f end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJIAAAAtCAYAAABF5zIuAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAABLpJREFUeNrtXG9klVEYPybXZMbkmsxEkkwyrslkEpNMZvo2SWYkM5nEZK5JYvZhMn3pU5KMmX1IJpLMzEQyM0nsQzIzI5lM5rLO036vvZ2d973v33NP931+/Nh97/vuPnvOc59/5zwTguGHPXBXclHyFKuEEQc1kgOSn1gVjCTwm1XAiIuLkvOsBkYcHEeOdDLFz9hBCGVUKU5LvoYxpQVK4ldY1dXtieYk6yNWfEHRIzllsBJlBKywHkhuomxfljyh3NMvOaZ59iHec0BGdMbAgo1KjkDuDST17zVeMKjcSRpSneS45Dr0OSvZkAVDojA0iT+WjGoa33gVVMo3ul73ST7RKF1lGoZEMq5JDrvknvDwUkHkTkquOnzeI3jlnOQ9yavVbkS9WBQ3nkt2ae69gsUidEq+q2AI+SrZolyjhdtOQe4wco3hS5k5UDhoV67Na0Kbg7co6yn8HUvAcMrRKxTvaK7XehhSWLnjyLWVlTBWroSmn3/53D+EuH+ugknteXwBVLT7eJs4cgeVq01yIauJ9pby+oLw3tag92YQJnoraEj02c801+9KFlOQO6hcXUisU8OAR+XgF2cHDBnSOkKCgyKUroIai68kjyKh/JhAaIu6YJNImN2gpHZFU7UlIXdQuQqSX9JaKHKlSxGeW0wpfOjK4KcIaZQXvUQJ70Ye19wLQFXIiwoZ0iyS7U68bsK1vpTkDpNsL6NiO4LkfwgeMVJSphpEawSlFgzG2xFUbkV4p01X+Z/DIjVpnptCRWQaJF83jKmExevReKhKyN2MYqUED9mfhKW2wpCiYgEGZRp5wTCKcoZE3c3BGL//TsjcilGlhvRGskPpcyxp3G0eSWBtiHKWkSFD2kasduOsJpmlLYrLmudzwrvBFrVpxrDUkPwWr+Tx3KCrvL9ZporYZTWzRyr5vEdVErXs18r0NXYNfQGY5phIaHPQASO55fM8hzb2SH9BG4W6ZlQNSvvryI+8wMk2G5Jv+U+HsZwu7A3Jxz651DirmQ1J15BsE4fP/0zAoFRUqiHJsMyQCNQ3cvbMahHudOdV5sS/54JMbpGkWdHyxG1CsH3TNm3wxG2CuC3CbXWMl6nm/kfwxC0jNrI6cUveuJGX/wBxJlpNTNzaCDqm8gNcFfvnkzKNOBOtJiZubQQZzbo4OIfWwr4o+kSrqYlbmyp0B9eEuSlgK0Fnmuk89E8kx3R2mwYJh1332DZxK5CHzEDmb8jJRASZk5JpVNFZ5hJDGvHpw8/1UMieOHyM1aaJ23qE3m5XGFnV3Gdq2nZW+Zt7s2ZIRY9vEZ2LbtIkkrZM3FKr5L5yjfKyXMIyh5GJJkmas+qRviO0qV5qx+N+WyZuKQznlWvbHlWmqWnbnawaEVUXuj6P10QrwZaJW90CL6Ygc9wp4EyAqgzdKU2viVZbJm4pL5oOeK+paVsvnWWmxNctCBmXulVj08QtbXJ/CHCfyWnbSVF921uBQQr+LA4aaAUkrNRUc/97G9smbgXkHkJu0oDEuyMFmcNUbV1Z7iE1QgnUi6HTCpfEfnvfGZGyceLW8TZ03KYEo3L3hSohs1tnDEYkkPfbYDUw4oCOS1P/iCejGbFQQPUbGH8Apz7dyStA800AAAF+dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPkY8L21pPjxtbz4oPC9tbz48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+eDwvbWk+PG1vPik8L21vPjxtbz49PC9tbz48bWZyYWM+PG1yb3c+PG1pPmE8L21pPjxtc3VwPjxtaT54PC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bWk+YjwvbWk+PG1pPng8L21pPjxtbz4rPC9tbz48bWk+YzwvbWk+PC9tcm93Pjxtcm93PjxtaT5kPC9taT48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1pPmU8L21pPjxtaT54PC9taT48bW8+KzwvbW8+PG1pPmY8L21pPjwvbXJvdz48L21mcmFjPjwvbWF0aD5qcZ6/AAAAAElFTkSuQmCC)
The correct answer is: y = a / d
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.
For the given function both the polynomials have the same degree, divide the coefficients of the leading terms.
y = a / d
Related Questions to study
Are graphs of the equations parallel, perpendicular or neither?
y = 2x + 1; 2x - y = 3
Are graphs of the equations parallel, perpendicular or neither?
y = 2x + 1; 2x - y = 3
A Trainer mixed water with an electrolyte solution. Container is having 12 gal of 25% electrolyte solution. The Concentration of electrolytes can be modelled by
, Graph the function.
A Trainer mixed water with an electrolyte solution. Container is having 12 gal of 25% electrolyte solution. The Concentration of electrolytes can be modelled by
, Graph the function.
Find the 12th term. -8, -5.5 , -3, -0.5, 2.0,....
Find the 12th term. -8, -5.5 , -3, -0.5, 2.0,....
Write an equation of a line that passes through the given line and is perpendicular to the given line.
![left parenthesis 4 comma 3 right parenthesis semicolon space 4 x minus 5 y equals 30](data:image/png;base64,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)
Write an equation of a line that passes through the given line and is perpendicular to the given line.
![left parenthesis 4 comma 3 right parenthesis semicolon space 4 x minus 5 y equals 30](data:image/png;base64,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)
Write recursive formula. -5,-8.5,-12,-15.5,-19,....
Write recursive formula. -5,-8.5,-12,-15.5,-19,....
Write an equation of a line that passes through the given line and is perpendicular to the given line.
![left parenthesis negative 2 comma 5 right parenthesis semicolon space x equals 3](data:image/png;base64,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)
Write an equation of a line that passes through the given line and is perpendicular to the given line.
![left parenthesis negative 2 comma 5 right parenthesis semicolon space x equals 3](data:image/png;base64,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)
Find the vertical and horizontal asymptotes of rational function, then graph the function.
![straight F left parenthesis straight x right parenthesis equals fraction numerator x minus 1 over denominator 2 x plus 1 end fraction](data:image/png;base64,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)
Find the vertical and horizontal asymptotes of rational function, then graph the function.
![straight F left parenthesis straight x right parenthesis equals fraction numerator x minus 1 over denominator 2 x plus 1 end fraction](data:image/png;base64,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)
Write recursive formula. 2,6,10,14,18,....
Write recursive formula. 2,6,10,14,18,....
Write an equation of a line that passes through the given line and is perpendicular to the given line.
![left parenthesis 0 comma 3 right parenthesis semicolon space 3 x minus 4 y equals negative 8](data:image/png;base64,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)
Write an equation of a line that passes through the given line and is perpendicular to the given line.
![left parenthesis 0 comma 3 right parenthesis semicolon space 3 x minus 4 y equals negative 8](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJEAAAARCAYAAADdaE77AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAA0lJREFUeNrtWV9kW1EYP6aiZkbN1PRh1J5mIuRpYiZM1VRUqdnDzJSpicn7zB5mxExMzaipmZkwtYeZKFMVNRVmpqam1B72MH3ZQ9VElOz77Je5+Zxzc+7Nzc3NlR8/knPP+c65537n+3eUascdYlGFgyLmGyJGSBK3Qp7zE+YdIibgD5oSbSeJz4k1cBltnZAlVoh/iHXiLvEp8ZTolyZu+lirrfx+Y4bYjIFuHCcuEQ+x32vECdkpBSWSWCfmxKasW0y6QZwjJsQca5q+m1AmL/Aiv184QdyJiRKtEB8RR7DnRRiVNjwm5kXbPLRPgk/8dZ+LOdC03Q0wDjuI0Maz1V6IiRLVxf9jxIbsxCf4kmhbJU4ZXMmqj4VMEr9r2i9aWje/8hcMSvoQz3qBjOOdmoaTfU3TXsCJjxoOYVmdSvRTd4ITou23pk2hbd/DAsaJtxC3XDXIc1qQMjZ+NiD5jC/o1wL3f9ajDef32SaedVGim7D+Mu7YNcR1TQv2EkvwGM6D/0R2OtIMPHIR2rCYWL5kwVKerRJ5kT9NLOH3lYAsn1vpIi/WKcHK/la0PSDej3Dm3gCrxF8az+VZieoeFjAGheBA7HIXStmNfMZHPP9qkcX5PflJTYKi68vzf3P8P03cI472UBH8vhNb1DfEMw7PlMZ6k53c2b7BnY16dGfObKVm4c66yYZqLs8LUNZe1qV4/nMWSqRQnmih1MGS9tOdvTPsWRZZctspzWgC62nN4CmfgbXJggUVWLtZyAzWXOoiswzitMvSxiS4h2B1EDIz4zNdis91mBeagS99fogkAkeJvCbIVAHK54/0HoErW6vPKtyipMlKvFL/anDsKm5EOL3f0VhXxnnERv9hKjZuwMy2ikz3EFipDoFwFXWmEZwwNn0/kJUozYlMewysbeVzrFERSsMF09cRUKICUv3tiNeI5qBIWex1a7/Zei7Kzlsa3zeGF63Dhy+LeoHpo3Pk/gHj6lDGGc0CddceNkpkIz8Bfz6hGV82uOowlWgWz3Iq+phHmaSB/a6avk83F7BllxqNG0wXsH7lDRJyKvwL71CwqLxfQaSQro54HMdx0O0A5Q0aKkgqhoC7GI+wvCjiAtxxLPAXqWL6+lPCOmAAAADodEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPig8L21vPjxtbj4wPC9tbj48bW8+LDwvbW8+PG1uPjM8L21uPjxtbz4pPC9tbz48bW8+OzwvbW8+PG1vPiYjeEEwOzwvbW8+PG1uPjM8L21uPjxtaT54PC9taT48bW8+JiN4MjIxMjs8L21vPjxtbj40PC9tbj48bWk+eTwvbWk+PG1vPj08L21vPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjg8L21uPjwvbWF0aD6hIQiSAAAAAElFTkSuQmCC)
Tell whether the given sequence is an arithmetic sequence. -6,5,16,27,38,....
Tell whether the given sequence is an arithmetic sequence. -6,5,16,27,38,....
Tell whether the given sequence is an arithmetic sequence. 48,45,42,39,....
Tell whether the given sequence is an arithmetic sequence. 48,45,42,39,....
Find the vertical and horizontal asymptotes of rational function, then graph the function.
![straight F left parenthesis straight x right parenthesis equals fraction numerator x plus 2 over denominator x minus 3 end fraction](data:image/png;base64,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)
Find the vertical and horizontal asymptotes of rational function, then graph the function.
![straight F left parenthesis straight x right parenthesis equals fraction numerator x plus 2 over denominator x minus 3 end fraction](data:image/png;base64,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)
Which sequence is an arithmetic sequence?
Which sequence is an arithmetic sequence?
Write an equation of a line that passes through the given line and is perpendicular to the given line.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbgAAAAyCAYAAAAuls65AAABPUlEQVR4nO3bMYqEMACF4VVXPIqVjfe/hacRwUy/hB2LjDKP7ytDitf9BLQrpZQfAAjTPz0AAD5B4ACIJHAARBI4ACIJHACRBA6ASAIHQCSBAyCSwAEQSeAAiCRwAEQSOAAiCRwAkQQOgEgCB0AkgQMgksABEEngAIgkcABEEjgAIv3WDpdluXsHALy1bdvlu10ppfw9HMex6SAAaOE4jst3qy+4eZ6bjQGAJ1QDNwzD3TsAoKlq4PretycAfDeBAyBSNXBd1929AwCa8lQDIFL1BXee5907AKCp6n9w0zQ9sQUA/rXv++W71Rfcuq7NxgDAE6ovOAD4dj4yASCSwAEQSeAAiCRwAEQSOAAiCRwAkQQOgEgCB0AkgQMgksABEEngAIgkcABEEjgAIgkcAJEEDoBIAgdAJIEDINILyn0dfvj+7mMAAAAASUVORK5CYII=)
![left parenthesis negative 6 comma negative 3 right parenthesis semicolon y equals negative 2 over 5 x](data:image/png;base64,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)
Write an equation of a line that passes through the given line and is perpendicular to the given line.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbgAAAAyCAYAAAAuls65AAABPUlEQVR4nO3bMYqEMACF4VVXPIqVjfe/hacRwUy/hB2LjDKP7ytDitf9BLQrpZQfAAjTPz0AAD5B4ACIJHAARBI4ACIJHACRBA6ASAIHQCSBAyCSwAEQSeAAiCRwAEQSOAAiCRwAkQQOgEgCB0AkgQMgksABEEngAIgkcABEEjgAIv3WDpdluXsHALy1bdvlu10ppfw9HMex6SAAaOE4jst3qy+4eZ6bjQGAJ1QDNwzD3TsAoKlq4PretycAfDeBAyBSNXBd1929AwCa8lQDIFL1BXee5907AKCp6n9w0zQ9sQUA/rXv++W71Rfcuq7NxgDAE6ovOAD4dj4yASCSwAEQSeAAiCRwAEQSOAAiCRwAkQQOgEgCB0AkgQMgksABEEngAIgkcABEEjgAIgkcAJEEDoBIAgdAJIEDINILyn0dfvj+7mMAAAAASUVORK5CYII=)
![left parenthesis negative 6 comma negative 3 right parenthesis semicolon y equals negative 2 over 5 x](data:image/png;base64,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)
When will the graph of a rational function have no vertical asymptotes ? Give an example of such a function.
Let's say that r is a rational function.
Identify R's domain.
If necessary, reduce r(x) to its simplest form.
Find the x- and y-intercepts of the y=r(x) graph if one exists.
If the graph contains any vertical asymptotes or holes, locate where they are.
Then, identify and, if necessary, analyze r's behavior on each side of the vertical asymptotes.
Investigate R's final behavior. If one exists, locate the horizontal or slant asymptote.
The graph of y=r(x) can be drawn using a sign diagram and additional points if necessary.
When will the graph of a rational function have no vertical asymptotes ? Give an example of such a function.
Let's say that r is a rational function.
Identify R's domain.
If necessary, reduce r(x) to its simplest form.
Find the x- and y-intercepts of the y=r(x) graph if one exists.
If the graph contains any vertical asymptotes or holes, locate where they are.
Then, identify and, if necessary, analyze r's behavior on each side of the vertical asymptotes.
Investigate R's final behavior. If one exists, locate the horizontal or slant asymptote.
The graph of y=r(x) can be drawn using a sign diagram and additional points if necessary.