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Date	May Specimen paper	Marks available	5	Reference code	SPM.1.AHL.TZ0.4
Level	Additional Higher Level	Paper	Paper 1 (without calculator)	Time zone	Time zone 0
Command term	Sketch	Question number	4	Adapted from	N/A

Question

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

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

Markscheme

no $y$ $y$ values below 1 A1

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

(±1,1) local minima A1

(0,5) local maximum A1

smooth curve and smooth stationary points A1

[5 marks]

Examiners report

[N/A]

Syllabus sections

Topic 2—Functions » AHL 2.16—Graphing modulus equations and inequalities

19M.1.AHL.TZ2.H_11b:
State the range of $g$ $g$ .
19M.1.AHL.TZ2.H_11c:
Sketch the graphs of $y = f\left( x \right)$ $y = f\left( x \right)$ and $y = g\left( x \right)$ $y = g\left( x \right)$ on the same axes, clearly stating the points of intersection with any axes.
17M.1.AHL.TZ2.H_9a.i:
Showing any $x$ $x$ and $y$ $y$ intercepts, any maximum or minimum points and any asymptotes, sketch the following curves on separate axes.

$y = f(x)$ $y = f(x)$ ;
19M.1.AHL.TZ2.H_11d:
Find the coordinates of P.
22M.1.AHL.TZ2.3d:
Solve the inequality $0 < \frac{2 |x| - 1}{|x| + 1} < 2$ $0 < \frac{2 |x| - 1}{|x| + 1} < 2$ .
19M.1.AHL.TZ2.H_11a:
Describe the transformation by which $f\left( x \right)$ $f\left( x \right)$ is transformed to $g\left( x \right)$ $g\left( x \right)$ .
22M.1.AHL.TZ2.11a:
Sketch the curve $y = f (x)$ $y = f (x)$ , clearly indicating any asymptotes with their equations. State the coordinates of any local maximum or minimum points and any points of intersection with the coordinate axes.

Topic 2—Functions

Question

Markscheme

Examiners report

Syllabus sections

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