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(x)y=f(x). The graph has a horizontal asymptote at y=−1y=−1. The graph crosses the xx-axis at x=−1x=−1 and x=1x=1, and the yy-axis at y=2y=2.
On the following set of axes, sketch the graph of y=[f(x)]2+1y=[f(x)]2+1, clearly showing any asymptotes with their equations and the coordinates of any local maxima or minima.
Markscheme
no yy values below 1 A1
horizontal asymptote at y=2y=2 with curve approaching from below as x→±∞x→±∞ A1
(±1,1) local minima A1
(0,5) local maximum A1
smooth curve and smooth stationary points A1
[5 marks]