The following diagram shows the graph of $y=f\left(x\right)$. The graph has a horizontal asymptote at $y=-1$. The graph crosses the $x$-axis at $x=-1$ and $x=1$, and the $y$-axis at $y=2$.

On the following set of axes, sketch the graph of $y={\left[f\left(x\right)\right]}^2+1$, clearly showing any asymptotes with their equations and the coordinates of any local maxima or minima.

no $y$ values below 1        A1

horizontal asymptote at $y=2$ with curve approaching from below as $x\to \pm \mathrm{\infty }$        A1

(±1,1) local minima        A1

(0,5) local maximum        A1

smooth curve and smooth stationary points        A1

[5 marks]