Maths-
General
Easy
Question
Identify the asymptotes and sketch the graph of ![straight g left parenthesis straight x right parenthesis equals fraction numerator straight x squared minus 5 straight x plus 6 over denominator 2 straight x squared minus 10 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 .
The correct answer is: The vertical asymptote of the rational function is x = 2.24 and x = -2.24 . horizontal asymptote is y = (leading coefficient of numerator) / (leading coefficient of denominator) = 1/2=0.5
- Find the asymptotes of the rational function, if any.
- Draw the asymptotes as dotted lines.
- Find the x -intercept (s) and y -intercept of the rational function, if any.
- Find the values of y for several different values of x .
- 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 .
2x2 - 10 = 0
2x2 = 10
x2 = 5
x = 2.24 or x = -2.24
The vertical asymptote of the rational function is x= 2.24 and x= -2.24 .
We will find more points on the function and graph the function.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) =
=0.5
Related Questions to study
Maths-
Write recursive formula and find the first term. ![a subscript n equals 108 minus n](data:image/png;base64,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)
Write recursive formula and find the first term. ![a subscript n equals 108 minus n](data:image/png;base64,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)
Maths-General
Maths-
Are graphs of the equations parallel, perpendicular or neither?
![y equals 4 x plus 1 space straight & space y equals negative 4 x minus 2](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALgAAAAPCAYAAABX/AUKAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAoxJREFUeNrtWUFEZVEYvp5kpM140mIWkYxkPG+bWYwhIxmZzRhPRka0ynjazCpJhrRoMRJJi2REnpGMDHlGMkYkeZIRadlimMUskgz1/dMXt+u+d8/t3c7733U/Pt13uofj+79z/v8/13Fqi5fgpaMHj8ExcD/kvEdgEbzg3KwTb2iJ21OwAP51aT+gRaRm8FCZwZfB4Tus6Qf4nM8vwF8xNremuG2BOa5J0MVY5DQINQ8O3bNQl5bmyemR4rP8PYuxwW3ErRq0gSXv4CL4xuflPPjxnlJLMcBMIuKUz/gk/6fJ4N/BPj5LipwzmGNb83qKW7U49w4MgtOesSbwCEyXMUAQy6GRO6zNwEx7YKvr9ztwVuEJ3gOeMGV+AhsM5tjUPArYjFs16GaZcgty+qx6xsbZcEUN2d0jhmbqBWdcJioqLFHEqKfgbwbSFDY1r7e43RUPwB1mmluQE+PA9bsFPOaEKJHx2V1BZtoEn7FDThsYM4pTzvS91+A38CE4yueKqbIGmkehTz3ETWKwxibfF+7GaIa1YNQLkt3VEVKoPJu4jMImc4/GdFiWiEGzrnKjFDDfhuZRwHbcwqKd5u6o9NI2X2xnoFI1OEH8mpoCg59TaPALj079NMNN6TIeMN+G5vUYtzDoBBd4oFTEEgP0GXxrWbxyu3KdC5d7zl2DVGfb4H4fFqSufs+blbRSzbXHzRSt1Nukqf+fUhYN0qoNoSTtb3iEka9ny8oMLub841xf96Uo9AfwH2tQrZprj5spvvIEN8IrLrq/xkLJddQX5/rztxcr7NBtpmKT25BdmvqcNwYTnDuhVPO4xC1UPyIi/3QS2ESiuUVIaulOZEg0jyOesJ5JkGgeK1wBL7UM/qb/si0AAAEQdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPnk8L21pPjxtbz49PC9tbz48bW4+NDwvbW4+PG1pPng8L21pPjxtbz4rPC9tbz48bW4+MTwvbW4+PG1vPiYjeEEwOzwvbW8+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPiZhbXA7PC9taT48bW8+JiN4QTA7PC9tbz48bWk+eTwvbWk+PG1vPj08L21vPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjQ8L21uPjxtaT54PC9taT48bW8+JiN4MjIxMjs8L21vPjxtbj4yPC9tbj48L21hdGg+jbTnAgAAAABJRU5ErkJggg==)
Are graphs of the equations parallel, perpendicular or neither?
![y equals 4 x plus 1 space straight & space y equals negative 4 x minus 2](data:image/png;base64,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)
Maths-General
Maths-
Write recursive formula and find the first term. ![a subscript n equals 10 plus 8 n](data:image/png;base64,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)
Write recursive formula and find the first term. ![a subscript n equals 10 plus 8 n](data:image/png;base64,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)
Maths-General
Maths-
Are graphs of the equations parallel, perpendicular or neither?
![x minus 3 y equals 6 space straight & space x minus 3 y equals 9](data:image/png;base64,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)
Are graphs of the equations parallel, perpendicular or neither?
![x minus 3 y equals 6 space straight & space x minus 3 y equals 9](data:image/png;base64,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)
Maths-General
Maths-
What is the graph of ![f left parenthesis x right parenthesis equals fraction numerator 4 x squared minus 9 over denominator x squared plus 2 x minus 15 end fraction](data:image/png;base64,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)
What is the graph of ![f left parenthesis x right parenthesis equals fraction numerator 4 x squared minus 9 over denominator x squared plus 2 x minus 15 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Find the equation for a path that passes through the point (-4, 9) and is parallel to
.
Find the equation for a path that passes through the point (-4, 9) and is parallel to
.
Maths-General
Maths-
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript minus 7 semicolon a subscript 1 equals negative 3](data:image/png;base64,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)
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript minus 7 semicolon a subscript 1 equals negative 3](data:image/png;base64,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)
Maths-General
Maths-
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript plus 1 semicolon a subscript 1 equals 12](data:image/png;base64,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)
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript plus 1 semicolon a subscript 1 equals 12](data:image/png;base64,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)
Maths-General
Maths-
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript minus 21 semicolon a subscript 1 equals 56](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKsAAAARCAYAAACiuVwKAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAArFJREFUeNrtWc8rRFEUfk2TJCmLSZqFkibJQkmSZCNJFlLSZKkkSxsLWch/YCcLSVKSJNlJkoWSJAspSwspC0mSGufkU9d157kz8+679z3z1be4b+7MnHPPOff8eJ5XRtjoJm4Tn4nvxEviuM/+DHEe+6KInA9V6CBu4XzeiHvE3rLb2MExMUusxrqFeIpnKqwTJ32MGwVn1cUknDODdQ0C+aTsNu6ggXgVoNGj6KwctOe6P5ogLhAfhPTUYElBl2QJC28BO6srZ6gr97JPdvmFfeISsRaKct0wbKhWyf2hRNCyuI4ulALFGH0Tnw07ak9dZ70h1utszEIZEWvEQQuGc0mWMFBJPEPjFZSzunSGOdzs3DAdEGeEel3OLFyr7hBf8Z1zVfN5hOiWGwEbacMlWUxljm/wrbdL7A+4UXHxDJPEdkw2+BZtVuh3gYBKIhtwAN8Sp8WNr/hQrHdeLBnThCwuohGO2mSgq3bJnir0I3hE8M2bVuxtI96LDx6lDd3wchuwLUsYc02+VVaIVYZGQIWcoa05rtxQHkgBJuJdXNyjdvoGC79tyVlty2J6rlmHejJpqKsu9AxtzHFbiXfSM071Y3kC+0x8sIjRQQJ1zQY8PV/XNoTilz1+NmBFXJHFlPH2FfVaKfKoGqxCztC0vjuonxPgABx1RNpXgdJgQgjkTu9r/twn/+gcIn4eUfmgGHXwn30gGtOoJ54MKOiCLKaMV8zox29fvtGVzhmGoe8omqQP2Idl6sizN4Xy6AX72Xl7dP4kpXjW6f18y8C10GEIaaMUWYptCKL0xmhTYyyVipG+WuD53Zq0Xo2pLFExHmeU6yJq4Ng7K78RmZLWEzGVJSrGS6Np88rO+rtYFtPNrmfvzZJpWWJnvP+m75M0EpHXcZCllGF3VJ00Evp+ApffGAAm70tJAAABD3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3ViPjxtaT5hPC9taT48bWk+bjwvbWk+PC9tc3ViPjxtbz49PC9tbz48bXN1Yj48bWk+YTwvbWk+PG1yb3c+PG1pPm48L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjE8L21uPjwvbXJvdz48L21zdWI+PG1vPiYjeDIyMTI7PC9tbz48bW4+MjE8L21uPjxtbz47PC9tbz48bXN1Yj48bWk+YTwvbWk+PG1uPjE8L21uPjwvbXN1Yj48bW8+PTwvbW8+PG1uPjU2PC9tbj48L21hdGg+xu/rJwAAAABJRU5ErkJggg==)
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript minus 21 semicolon a subscript 1 equals 56](data:image/png;base64,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)
Maths-General
Maths-
Graph each function ![g left parenthesis x right parenthesis equals fraction numerator 3 x plus 2 over denominator x minus 1 end fraction](data:image/png;base64,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)
Graph each function ![g left parenthesis x right parenthesis equals fraction numerator 3 x plus 2 over denominator x minus 1 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Find the equation for a path that passes through the point (6, 6) and is perpendicular to
.
Find the equation for a path that passes through the point (6, 6) and is perpendicular to
.
Maths-General
Maths-
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript minus 2 semicolon a subscript 1 equals negative 1](data:image/png;base64,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)
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript minus 2 semicolon a subscript 1 equals negative 1](data:image/png;base64,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)
Maths-General
Maths-
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript plus 6 semicolon a subscript 1 equals 9](data:image/png;base64,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)
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript plus 6 semicolon a subscript 1 equals 9](data:image/png;base64,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)
Maths-General
Maths-
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript plus 15 semicolon a subscript 1 equals 8](data:image/png;base64,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)
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript plus 15 semicolon a subscript 1 equals 8](data:image/png;base64,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)
Maths-General
Maths-
Graph each function ![f left parenthesis x right parenthesis equals fraction numerator 4 x minus 3 over denominator x plus 8 end fraction](data:image/png;base64,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)
Graph each function ![f left parenthesis x right parenthesis equals fraction numerator 4 x minus 3 over denominator x plus 8 end fraction](data:image/png;base64,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)
Maths-General