DP Mathematics: Analysis and Approaches Questionbank

SL 2.8—Reciprocal and simple rational functions, equations of asymptotes
Description
[N/A]Directly related questions
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21N.1.SL.TZ0.3b.i:
the xx-axis.
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21N.1.SL.TZ0.3c:
Sketch the graph of ff on the axes below.
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21N.1.SL.TZ0.3a.i:
the vertical asymptote of the graph of ff.
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21N.1.SL.TZ0.3a.ii:
the horizontal asymptote of the graph of ff.
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21N.1.SL.TZ0.3b.ii:
the yy-axis.
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21N.1.AHL.TZ0.2d:
The function gg is defined by g(x)=ax+43-xg(x)=ax+43−x, where x∈ℝ, x≠3 and a∈ℝ.
Given that g(x)=g-1(x), determine the value of a.
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21N.1.AHL.TZ0.2a.i:
the vertical asymptote of the graph of f.
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21N.1.AHL.TZ0.2b.ii:
the y-axis.
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21N.1.AHL.TZ0.2a.ii:
the horizontal asymptote of the graph of f.
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21N.1.AHL.TZ0.2b.i:
the x-axis.
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21N.1.AHL.TZ0.2c:
Sketch the graph of f on the axes below.
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22M.1.SL.TZ2.4a.i:
Write down the equation of the vertical asymptote.
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22M.1.SL.TZ2.4b:
On the set of axes below, sketch the graph of y=f(x).
On your sketch, clearly indicate the asymptotes and the position of any points of intersection with the axes.
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22M.1.SL.TZ2.4c:
Hence, solve the inequality 0<2x-1x+1<2.
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22M.1.SL.TZ2.4a.ii:
Write down the equation of the horizontal asymptote.
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22M.1.AHL.TZ2.3a.i:
Write down the equation of the vertical asymptote.
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22M.1.AHL.TZ2.3a.ii:
Write down the equation of the horizontal asymptote.
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22M.2.SL.TZ1.8a.i:
write down the equation of the vertical asymptote.
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22M.2.SL.TZ1.8a.ii:
find the equation of the horizontal asymptote.
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22M.1.AHL.TZ2.3c:
Hence, solve the inequality 0<2x-1x+1<2.
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18N.2.AHL.TZ0.H_8a:
On the following axes, sketch the two possible graphs of y=f(x) giving the equations of any asymptotes in terms of p and q.
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18N.2.AHL.TZ0.H_8b:
Given that p=43, q=49 and A has coordinates (−12,0), determine the possible sets of values for a, b and c.
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18M.2.SL.TZ2.S_7b:
Write down the equation of the horizontal asymptote to the graph of f.
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18N.2.SL.TZ0.S_3a.i:
For the graph of f, find the y-intercept.
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18N.2.SL.TZ0.S_3b:
Hence or otherwise, write down limx→∞(6x−12x+3).
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19M.1.AHL.TZ2.H_5a:
Sketch the graph of y=x−42x−5, stating the equations of any asymptotes and the coordinates of any points of intersection with the axes.
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18M.1.AHL.TZ2.H_10b.i:
Express g(x) in the form A+Bx−2 where A, B are constants.