Practice section 6 of 9

Use a graphing calculator to sketch (a)(i) $y=x+2$, (ii) $y=1/(x+2)$; (b)(i) $y=(x+1)(x-3)$, (ii) $y=1/((x+1)(x-3))$. By comparing each pair, what do you observe about the relationship between $y=f(x)$ and $y=1/f(x)$?

Given the three graphs of $y=f(x)$, sketch the corresponding graphs of $y=1/f(x)$. Indicate, if possible, the coordinates of the turning points, axial intercepts and asymptotes.

The curve shown has equation $y=f(x)$. On a separate diagram, sketch $y=1/f(x)$, indicating clearly the asymptotes and the coordinates of points corresponding to $A(3,-1)$ and $B(1,0)$ where applicable.

Given $f(x)=x+4$, sketch $y=1/f(x)$.

The graph of $y=f(x)$ is shown, with $A(-1,0)$, $B(-0.549,-0.631)$, $C(0,0)$, $D(1.215,2.113)$ and $E(2,0)$. On separate diagrams, sketch (a) $y=f(x-2)$, (b) $y=f(-x)+1$, (c) $y=f(2x+1)$, (d) $y=2f(|x|)$, (e) $y=f(-|x|)$, (f) $y=|f(x-2)|$, (g) $y=f(|x-2|)$, (h) $y=1/f(x)$. Indicate clearly, if possible, all coordinates of points corresponding to A, B, C, D and E.

Explain how the graph of $y=2/(3x-1)$ may be obtained from $y=1/x$ by appropriate transformations.