| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Single transformation application |
| Difficulty | Easy -1.3 This question tests basic function transformations with straightforward applications: sketching a simple reciprocal function, applying a horizontal translation (standard substitution x→x-2), and finding the image of a point under a vertical stretch. All three parts require only direct recall of transformation rules with no problem-solving or synthesis required. |
| Spec | 1.02o Sketch reciprocal curves: y=a/x and y=a/x^21.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Curve in both quadrants, correct shape, symmetrical, not touching axis, asymptote the axes, not finite | B1 | Curve must be symmetrical, allow slight movement away from asymptote at one end but not more |
| Answer | Marks | Guidance |
|---|---|---|
| \(y = -\dfrac{1}{(x-2)^2}\) | M1, A1 | M1 for \((y=)-\dfrac{1}{(x-2)^2}\) or \((y=)-\dfrac{1}{(x+2)^2}\); A1 fully correct, must include '\(y=\)' |
| Answer | Marks | Guidance |
|---|---|---|
| \(\left(\dfrac{1}{2}, -2\right)\) | B2 | B1 for each coordinate |
# Question 3:
## Part (a):
Curve in both quadrants, correct shape, symmetrical, not touching axis, asymptote the axes, not finite | **B1** | Curve must be symmetrical, allow slight movement away from asymptote at one end but not more
## Part (b):
$y = -\dfrac{1}{(x-2)^2}$ | **M1, A1** | M1 for $(y=)-\dfrac{1}{(x-2)^2}$ or $(y=)-\dfrac{1}{(x+2)^2}$; A1 fully correct, must include '$y=$'
## Part (c):
$\left(\dfrac{1}{2}, -2\right)$ | **B2** | B1 for each coordinate
---3
\begin{enumerate}[label=(\alph*)]
\item Sketch the curve $y = - \frac { 1 } { x ^ { 2 } }$.
\item 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.
\item 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 $P$.
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q3 [5]}}