1. The document discusses reciprocal functions of the form y=1/x and provides steps for graphing them. 2. When x is 0, 1/x is undefined, when x is positive 1/x is positive, and when x is negative 1/x is negative. 3. As x becomes large, 1/x approaches 0, and as x approaches 0, 1/x becomes very large.

1. Reciprocal Functions
1
1. Graph y .
x
x y
0 1
= undefined
0
1
2
10
100
0.5
0.1
0.01
1
When x is 0, is _______________.
x
1 1
When x is positive, is _______________. When x is negative, is
x x
_______________.
1 1
When x becomes large, _______________. When x approaches 0,
x x
_______________.
Steps:
1. Vertical Asymptotes
2. Signs
3. Invariant & Other Important Points
1
2. Given y f x , as shown, graph y .
f x

2. 2 1
3. Given f x x 1 , graph y f x and y .
f x
10
8
6
4
2
-10 -8 -6 -4 -2 2 4 6 8 10
-2
-4
-6
-8
-10
1
4. Given y f x , as shown, graph y .
f x

3. 1 1
5. Given f x x 2 , graph y f x and y .
2 f x
1
6. Given f x x x 2 , graph y f x and y .
f x