The diagram shows the graph of $y=\mathrm{f}(x)$. It has a turning point at $(1,-3)$, asymptotes

Question

The diagram shows the graph of $y=\mathrm{f}(x)$. It has a turning point at $(1,-3)$, asymptotes $x=-1$, $y=0$ and $y=2$, and crosses the origin. On the axes provided, sketch the graphs of $y=\mathrm{f}(-x)$,[2] $y=\mathrm{f}(|x|)+2$,[3] $y=\mathrm{f}'(x)$,[3] labelling clearly the equation(s) of any asymptote(s), coordinates of any axial intercept(s) and turning point(s) where applicable. State a sequence of transformations that will transform the curve with equation $y=\ln(8x^3)-1$ on to the curve with equation $y=\ln x$.[3]

Accepted Answer

(b) Translate by $\begin{pmatrix}0\1-\ln8\end{pmatrix}$, then scale parallel to the $y$-axis by factor $\frac13$

2026 EJC P1 Q8

2026 EJC P1 Q8

Solution:

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