Drawing the graph of the reciprocal function

1
Drawing the graph of the reciprocal function
2
Y
Whenever the original function is 0 the
reciprocal will be undefined so we need
asymptotes where the graph crosses the x-axis
Whenever the original function is 1 or 1 the
reciprocal will be also be 1 or 1 so we can
put points on the original graph where the
y-co-ord is 1 or 1. Also the vertex is at (2,
1.5) so the vertex of the reciprocal will be at
(2, 0.67)
If x lt 0.8 For the original x ? ? y ? ? For
the reciprocal x ? ? y ? 0 For the
original x ? 0.8 then y ? 0 For the
reciprocal x ? 0.8 y ? ?
If x gt 3.2 For the original x ? ? y ? ? For
the reciprocal x ? ? y ? 0 For the
original x ? 3.2 then y ? 0 For the
reciprocal x ? 3.2 y ? ?
10
5
If 0.8 lt x lt 3.2 For the original x ? 0.8 then
y ? 0 For the reciprocal x ? 0.8 then y ?
? For the original x ? 3.2 then y ? 0 For the
reciprocal x ? 3.2 then y ? ?
X
-2
-1
1
2
3
4
5
-5
-10
3
Your turn

• This time you explain why the graph of the
  reciprocal looks the way that it does!

4
Y
10
5
X
-2
-1
1
2
3
4
5
-5
-10