Moderate -0.8 This is a straightforward function transformation question requiring students to recognize that y = 3 - f(x) can be decomposed into a reflection in the x-axis followed by a translation of 3 units upward (or equivalently described in reverse order). It tests basic understanding of composite transformations but requires minimal problem-solving beyond pattern recognition and recall of standard transformation rules.
1 The graph of \(y = \mathrm { f } ( x )\) is transformed to the graph of \(y = 3 - \mathrm { f } ( x )\).
Describe fully, in the correct order, the two transformations that have been combined.
Or Translation 3 units in the negative \(y\)-direction.
Then {Reflection} {in the \(x\)-axis} or {Stretch of scale factor \(-1\)} {parallel to \(y\)-axis}
\*B1 DB1
N.B. If order reversed a maximum of 3 out of 4 marks awarded.
Total: 4
## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| {Reflection} {[in the] $x$-axis} **or** {Stretch of scale factor $-1$} {parallel to $y$-axis} | **\*B1 DB1** | { } indicate how the B1 marks should be awarded throughout. |
| Then {Translation} $\left\{\begin{pmatrix} 0 \\ 3 \end{pmatrix}\right\}$ | **B1 B1** | Or Translation 3 units in the positive $y$-direction. **N.B.** If order reversed a maximum of 3 out of 4 marks awarded. |
**Alternative method for question 1:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| {Translation} $\left\{\begin{pmatrix} 0 \\ -3 \end{pmatrix}\right\}$ | **B1 B1** | Or Translation 3 units in the negative $y$-direction. |
| Then {Reflection} {in the $x$-axis} or {Stretch of scale factor $-1$} {parallel to $y$-axis} | **\*B1 DB1** | **N.B.** If order reversed a maximum of 3 out of 4 marks awarded. |
| | **Total: 4** | |
1 The graph of $y = \mathrm { f } ( x )$ is transformed to the graph of $y = 3 - \mathrm { f } ( x )$.\\
Describe fully, in the correct order, the two transformations that have been combined.\\
\hfill \mbox{\textit{CAIE P1 2021 Q1 [4]}}