Single transformation application

Questions that ask to find the equation after applying a single transformation (one translation, one stretch, or one reflection) to a given function.

7 questions

OCR C1 2005 January Q3
3
  1. The curve \(y = 5 \sqrt { } x\) is transformed by a stretch, scale factor \(\frac { 1 } { 2 }\), parallel to the \(x\)-axis. Find the equation of the curve after it has been transformed.
  2. Describe the single transformation which transforms the curve \(y = 5 \sqrt { } x\) to the curve \(y = ( 5 \sqrt { } x ) - 3\).
OCR C1 2013 June Q5
5
  1. Sketch the curve \(y = \frac { 2 } { x ^ { 2 } }\).
  2. The curve \(y = \frac { 2 } { x ^ { 2 } }\) is translated by 5 units in the negative \(x\)-direction. Find the equation of the curve after it has been translated.
  3. Describe a transformation that transforms the curve \(y = \frac { 2 } { x ^ { 2 } }\) to the curve \(y = \frac { 1 } { x ^ { 2 } }\).
OCR C1 2015 June Q2
2
  1. Sketch the curve \(y = - \frac { 1 } { x }\).
  2. The curve \(y = - \frac { 1 } { x }\) is translated by 2 units parallel to the \(x\)-axis in the positive direction. State the equation of the transformed curve.
  3. Describe a transformation that transforms the curve \(y = - \frac { 1 } { x }\) to the curve \(y = - \frac { 1 } { 3 x }\).
OCR PURE 2066 Q3
3
  1. Sketch the curve \(y = - \frac { 1 } { x ^ { 2 } }\).
  2. The curve \(y = - \frac { 1 } { x ^ { 2 } }\) is translated by 2 units in the positive \(x\)-direction. State the equation of the curve after it has been translated.
  3. The curve \(y = - \frac { 1 } { x ^ { 2 } }\) is stretched parallel to the \(y\)-axis with scale factor \(\frac { 1 } { 2 }\) and, as a result, the point \(\left( \frac { 1 } { 2 } , - 4 \right)\) on the curve is transformed to the point \(P\). State the coordinates of \(P\).
OCR MEI AS Paper 1 2018 June Q9
9 The curve \(y = ( x - 1 ) ^ { 2 }\) maps onto the curve \(\mathrm { C } _ { 1 }\) following a stretch scale factor \(\frac { 1 } { 2 }\) in the \(x\)-direction.
  1. Show that the equation of \(\mathrm { C } _ { 1 }\) can be written as \(y = 4 x ^ { 2 } - 4 x + 1\). The curve \(\mathrm { C } _ { 2 }\) is a translation of \(y = 4.25 x - x ^ { 2 }\) by \(\binom { 0 } { - 3 }\).
  2. Show that the normal to the curve \(\mathrm { C } _ { 1 }\) at the point \(( 0,1 )\) is a tangent to the curve \(\mathrm { C } _ { 2 }\).
AQA AS Paper 1 2021 June Q3
3 The graph of the equation \(y = \frac { 1 } { x }\) is translated by the vector \(\left[ \begin{array} { l } 3
0 \end{array} \right]\)
3
  1. Write down the equation of the transformed graph. 3
  2. State the equations of the asymptotes of the transformed graph.
AQA AS Paper 2 2024 June Q4
4 Curve \(C\) has equation \(y = 8 \sin x\) 4
  1. Curve \(C\) is transformed onto curve \(C _ { 1 }\) by a translation of vector \(\left[ \begin{array} { l } 0
    4 \end{array} \right]\)
    Find the equation of \(C _ { 1 }\) 4
  2. \(\quad\) Curve \(C\) is transformed onto curve \(C _ { 2 }\) by a stretch of scale factor 4 in the \(y\) direction. Find the equation of \(C _ { 2 }\) 4
  3. Curve \(C\) is transformed onto curve \(C _ { 3 }\) by a stretch of scale factor 2 in the \(x\) direction. Find the equation of \(C _ { 3 }\)