Sketch transformed curve from description

Questions that provide a graph of y = f(x) with key features marked and ask students to sketch a specific transformation (like y = f(x+a) or y = af(x)) on separate axes.

5 questions

Edexcel P1 2022 June Q4
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3cf69966-e825-4ff0-a6e8-c5dfdc92c53f-08_604_1207_251_370} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of a curve with equation \(y = \mathrm { f } ( x )\)
The curve has a minimum at \(P ( - 1,0 )\) and a maximum at \(Q \left( \frac { 3 } { 2 } , 2 \right)\)
The line with equation \(y = 1\) is the only asymptote to the curve. On separate diagrams sketch the curves with equation
  1. \(y = \mathrm { f } ( x ) - 2\)
  2. \(y = \mathrm { f } ( - x )\) On each sketch you must clearly state
    • the coordinates of the maximum and minimum points
    • the equation of the asymptote
Edexcel P1 2020 October Q5
5. (i) \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{dfb4b2bc-4bc8-4e5b-9b13-ffe4fbde1b4f-14_572_1025_212_463} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows a sketch of the curve with equation \(y = \mathrm { f } ( x )\).
The curve passes through the points \(( - 5,0 )\) and \(( 0 , - 3 )\) and touches the \(x\)-axis at the point \(( 2,0 )\). On separate diagrams sketch the curve with equation
  1. \(y = \mathrm { f } ( x + 2 )\)
  2. \(y = \mathrm { f } ( - x )\) On each diagram, show clearly the coordinates of all the points where the curve cuts or touches the coordinate axes.
    (ii) \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{dfb4b2bc-4bc8-4e5b-9b13-ffe4fbde1b4f-14_415_814_1548_571} \captionsetup{labelformat=empty} \caption{Figure 3}
    \end{figure} Figure 3 shows a sketch of the curve with equation $$y = k \cos \left( x + \frac { \pi } { 6 } \right) \quad 0 \leqslant x \leqslant 2 \pi$$ where \(k\) is a constant.
    The curve meets the \(y\)-axis at the point \(( 0 , \sqrt { 3 } )\) and passes through the points \(( p , 0 )\) and ( \(q , 0\) ). Find
  3. the value of \(k\),
  4. the exact value of \(p\) and the exact value of \(q\).
Edexcel P1 2018 Specimen Q6
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2217be5e-8edd-413f-9c97-212e585ff58d-12_440_679_269_630} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of the curve \(C\) with equation \(y = \mathrm { f } ( x )\) The curve \(C\) passes through the origin and through \(( 6,0 )\) The curve \(C\) has a minimum at the point \(( 3 , - 1 )\) On separate diagrams, sketch the curve with equation
  1. \(y = \mathrm { f } ( 2 x )\)
  2. \(y = \mathrm { f } ( x + p )\), where \(p\) is a constant and \(0 < p < 3\) On each diagram show the coordinates of any points where the curve intersects the \(x\)-axis and of any minimum or maximum points.
    a) \(( 6,0 ) \rightarrow ( 3,0 )\) $$( 3 , - 1 ) - 1 > ( 1.5 , - 1 )$$
    \includegraphics[max width=\textwidth, alt={}]{2217be5e-8edd-413f-9c97-212e585ff58d-12_616_772_1624_781}
    $$( 1.5 , - 1 )$$ \includegraphics[max width=\textwidth, alt={}, center]{2217be5e-8edd-413f-9c97-212e585ff58d-13_2261_50_312_39}
    \includegraphics[max width=\textwidth, alt={}, center]{2217be5e-8edd-413f-9c97-212e585ff58d-13_2637_1835_118_116}
Edexcel C12 2015 January Q3
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3b99072a-cd16-4c1d-9e44-085926a3ba24-05_645_933_258_463} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows a sketch of part of the curve with equation \(y = \mathrm { f } ( x )\).
The curve crosses the coordinate axes at the points ( \(2.5,0\) ) and ( 0,9 ), has a stationary point at ( 1,11 ), and has an asymptote \(y = 3\) On separate diagrams, sketch the curve with equation
  1. \(y = 3 \mathrm { f } ( x )\)
  2. \(y = \mathrm { f } ( - x )\) On each diagram show clearly the coordinates of the points of intersection of the curve with the two coordinate axes, the coordinates of the stationary point, and the equation of the asymptote.
Edexcel C12 2017 June Q7
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{08b1be3e-2d9a-4832-b230-d5519540f494-20_588_839_219_550} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows a sketch of part of the curve with equation \(y = \mathrm { f } ( x )\). The curve crosses the \(y\)-axis at the point \(( 0,8 )\). The line with equation \(y = 10\) is the only asymptote to the curve.
The curve has a single turning point, a minimum point at \(( 2,5 )\), as shown in Figure 3.
  1. State the coordinates of the minimum point of the curve with equation \(y = \mathrm { f } \left( \frac { 1 } { 4 } x \right)\)
  2. State the equation of the asymptote to the curve with equation \(y = \mathrm { f } ( x ) - 3\) The curve with equation \(y = \mathrm { f } ( x )\) meets the line with equation \(y = k\), where \(k\) is a constant, at two distinct points.
  3. State the set of possible values for \(k\).
  4. Sketch the curve with equation \(y = - \mathrm { f } ( x )\). On your sketch, show clearly the coordinates of the turning point, the coordinates of the intersection with the \(y\)-axis and the equation of the asymptote. \section*{\textbackslash section*\{D\}}