| Date | November 2010 | Marks available | 5 | Reference code | 10N.2.hl.TZ0.8 |
| Level | HL only | Paper | 2 | Time zone | TZ0 |
| Command term | Sketch | Question number | 8 | Adapted from | N/A |
Question
The diagram shows the graphs of a linear function f and a quadratic function g.
On the same axes sketch the graph of \(\frac{f}{g}\). Indicate clearly where the x-intercept and the asymptotes occur.
Markscheme
correct concavities A1A1
Note: Award A1 for concavity of each branch of the curve.
correct x-intercept of \(\frac{f}{g}\) (which is EXACTLY the x-intercept of f) A1
correct vertical asymptotes of \(\frac{f}{g}\) (which ONLY occur when x equals the x-intercepts of g) A1A1
[5 marks]
Examiners report
Many candidates answered well this question. Full marks were often achieved. Many other candidates did not attempt it at all.
Syllabus sections
Topic 2 - Core: Functions and equations » 2.2 » Investigation of key features of graphs, such as maximum and minimum values, intercepts, horizontal and vertical asymptotes and symmetry, and consideration of domain and range.
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