SPM.1.AHL.TZ0.4

pestleMathematicsAAHLPaper 1SPM· ahl-2-16-graphing-modulus-equations-and-inequalitiessource ↗

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.

Markscheme / solution

no $y$ values below 1 A1

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

(±1,1) local minima A1

(0,5) local maximum A1

smooth curve and smooth stationary points A1

[5 marks]

Examiners’ report

[N/A]