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<ol class="i-list"><li><div class="list-item-paragraph">The diagram shows the graph of $y=\mathrm{f}(x)$ which has a minimum point at $(0, 2)$ and asymptotes $x=2$ and $y=5.$</div><div class="list-item-paragraph">On separate diagrams, sketch the graphs of $y\ =\ \ \frac{1}{\mathrm{f}(x)}$.</div></li></ol>

The diagram shows the graph of $y=\mathrm{f}(x)$ which has a minimum point at $(0, 2)$ and asymptotes $x=2$ and $y=5.$

On separate diagrams, sketch the graphs of $y\ =\ \ \frac{1}{\mathrm{f}(x)}$.

Transformations of Graphs - General

Transformations of Graphs

International Baccalaureate Higher Level Mathematics

IB HL Math

2013 VJC P1 Q6 

**Left graph: $y = \mathrm{f}(x)$**
- Vertical asymptote at $x = 2$
- Horizontal asymptote at $y = 5$
- Maximum point marked at $x = 2$

**Right graph: $y = \frac{1}{\mathrm{f}(x)}$**
- Horizontal asymptote at $y = \frac{1}{5}$
- Vertical asymptote at $x = 3$ (where $\mathrm{f}(x) = 0$)
- Point $(0, \frac{1}{2})$ (reciprocal of $f(0) = 2$)
- Point $(1, 0)$ approximately
- Minimum point where $\mathrm{f}(x)$ has maximum

2013 VJC P1 Q6

2013 VJC P1 Q6

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