SPS SPS SM 2021 January — Question 2 9 marks

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2021
SessionJanuary
Marks9
TopicFunction Transformations
TypeMultiple separate transformations (sketch-based, standard transformations)
DifficultyModerate -0.8 This is a straightforward application of standard function transformations (horizontal translation, vertical translation, and vertical stretch) to clearly marked features. Students need only apply memorized transformation rules to given coordinates and the asymptote—no problem-solving, integration of multiple concepts, or novel insight required. Easier than average A-level questions.
Spec1.02w Graph transformations: simple transformations of f(x)
2.
\includegraphics[max width=\textwidth, alt={}]{fbe229f8-d390-487d-87fc-90edc50c3325-2_449_1130_842_440}
The figure above shows the graph of a curve with equation \(y = f ( x )\). The curve meets the \(x\) axis at \(( - 3,0 )\) and the \(y\) axis at \(( 0,2 )\). The curve has a maximum at \(( 3,4 )\) and a minimum at \(( - 3,0 )\). The line with equation \(y = 2\) is a horizontal asymptote to the curve. Sketch on separate diagrams the graph of ...
a) \(\ldots \quad y = f ( x + 3 )\).
b) \(. . \quad y = f ( x ) - 2\).
c) \(\ldots \quad y = \frac { 1 } { 2 } f ( x )\). Each of the sketches must include
  • the coordinates of any points where the graph meets the coordinate axes.
  • the coordinates of any minimum or maximum points of the curve.
  • any asymptotes to the curve, clearly labelled.
2.

\begin{center}
\includegraphics[max width=\textwidth, alt={}]{fbe229f8-d390-487d-87fc-90edc50c3325-2_449_1130_842_440}
\end{center}

The figure above shows the graph of a curve with equation $y = f ( x )$. The curve meets the $x$ axis at $( - 3,0 )$ and the $y$ axis at $( 0,2 )$. The curve has a maximum at $( 3,4 )$ and a minimum at $( - 3,0 )$.

The line with equation $y = 2$ is a horizontal asymptote to the curve.

Sketch on separate diagrams the graph of ...\\
a) $\ldots \quad y = f ( x + 3 )$.\\
b) $. . \quad y = f ( x ) - 2$.\\
c) $\ldots \quad y = \frac { 1 } { 2 } f ( x )$.

Each of the sketches must include

\begin{itemize}
  \item the coordinates of any points where the graph meets the coordinate axes.
  \item the coordinates of any minimum or maximum points of the curve.
  \item any asymptotes to the curve, clearly labelled.
\end{itemize}

\hfill \mbox{\textit{SPS SPS SM 2021 Q2 [9]}}
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