<ol class="i-list"><li><div class="list-item-paragraph">$y=\frac{1}{\mathrm{f}\left( x \right)}$</div></li><li><div class="list-item-paragraph">$y=\mathrm{f}'\left( x \right)$</div></li></ol>

Transformations of Graphs

International Baccalaureate Higher Level Mathematics

IB HL Math

Worked Example 1 (i)

Horizontal asymptote approaching $y = 2$

Since $1.999 < 2$, we have $\dfrac{1}{1.999} > \dfrac{1}{2}$

Vertical asymptotes at $x = 0$ and $x = 2$ (where $f(x) = 0$)

Horizontal asymptote at $y = \dfrac{1}{2}$

Maximum point at $\left(1, -\dfrac{1}{6}\right)$

$y = x \to y = \dfrac{1}{x}$ (reciprocal transformation)

Passes through $(1, 0)$ which corresponds to the steepest point (point of inflexion on $y = f(x)$)

Worked Example 1 (i)

Worked Example 1 (i)

Video Solution: