Sketch rational function from transformation

Questions asking to sketch a rational function by applying a transformation to a standard rational function (e.g., translating 1/x).

7 questions · Moderate -0.7

1.02o Sketch reciprocal curves: y=a/x and y=a/x^21.02w Graph transformations: simple transformations of f(x)
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CAIE P3 2015 November Q1
2 marks Easy -1.2
1 Sketch the graph of \(y = \mathrm { e } ^ { a x } - 1\) where \(a\) is a positive constant.
Edexcel P1 2021 January Q6
10 marks Standard +0.3
6. (a) Sketch the curve with equation $$y = - \frac { k } { x } \quad k > 0 \quad x \neq 0$$ (b) On a separate diagram, sketch the curve with equation $$y = - \frac { k } { x } + k \quad k > 0 \quad x \neq 0$$ stating the coordinates of the point of intersection with the \(x\)-axis and, in terms of \(k\), the equation of the horizontal asymptote.
(c) Find the range of possible values of \(k\) for which the curve with equation $$y = - \frac { k } { x } + k \quad k > 0 \quad x \neq 0$$ does not touch or intersect the line with equation \(y = 3 x + 4\) \includegraphics[max width=\textwidth, alt={}, center]{6a5d0ffc-a725-404b-842a-f3b6000e6fed-21_72_47_2615_1886}
Edexcel C1 2013 January Q6
12 marks Moderate -0.8
6.
[diagram]
Figure 1 shows a sketch of the curve with equation \(y = \frac { 2 } { x } , x \neq 0\) The curve \(C\) has equation \(y = \frac { 2 } { x } - 5 , x \neq 0\), and the line \(l\) has equation \(y = 4 x + 2\)
  1. Sketch and clearly label the graphs of \(C\) and \(l\) on a single diagram. On your diagram, show clearly the coordinates of the points where \(C\) and \(l\) cross the coordinate axes.
  2. Write down the equations of the asymptotes of the curve \(C\).
  3. Find the coordinates of the points of intersection of \(y = \frac { 2 } { x } - 5\) and \(y = 4 x + 2\)
Edexcel C1 2007 June Q5
5 marks Easy -1.2
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c0db3fe8-62ec-41e3-acaf-66b2c7b2754d-06_702_785_242_607} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of the curve with equation \(y = \frac { 3 } { x } , x \neq 0\).
  1. On a separate diagram, sketch the curve with equation \(y = \frac { 3 } { x + 2 } , x \neq - 2\), showing the coordinates of any point at which the curve crosses a coordinate axis.
  2. Write down the equations of the asymptotes of the curve in part (a).
OCR C1 2006 January Q4
7 marks Easy -1.2
4
  1. Sketch the curve \(y = \frac { 1 } { x ^ { 2 } }\).
  2. Hence sketch the curve \(y = \frac { 1 } { ( x - 3 ) ^ { 2 } }\).
  3. Describe fully a transformation that transforms the curve \(y = \frac { 1 } { x ^ { 2 } }\) to the curve \(y = \frac { 2 } { x ^ { 2 } }\).
AQA FP1 2008 June Q7
10 marks Moderate -0.3
7 A curve \(C\) has equation $$y = 7 + \frac { 1 } { x + 1 }$$
  1. Define the translation which transforms the curve with equation \(y = \frac { 1 } { x }\) onto the curve \(C\).
    1. Write down the equations of the two asymptotes of \(C\).
    2. Find the coordinates of the points where the curve \(C\) intersects the coordinate axes.
  3. Sketch the curve \(C\) and its two asymptotes.
OCR MEI C1 Q6
11 marks Moderate -0.3
  1. \includegraphics{figure_1} Fig. 10 shows a sketch of the graph of \(y = \frac{1}{x}\). Sketch the graph of \(y = \frac{1}{x-2}\), showing clearly the coordinates of any points where it crosses the axes. [3]
  2. Find the value of \(x\) for which \(\frac{1}{x-2} = 5\). [2]
  3. Find the \(x\)-coordinates of the points of intersection of the graphs of \(y = x\) and \(y = \frac{1}{x-2}\). Give your answers in the form \(a \pm \sqrt{b}\). Show the position of these points on your graph in part (i). [6]