Reciprocal Functions

1. Graph 1

yx

.

x y

0 1

0= undefined

1

2

10

100

0.5

0.1

0.01

When x is 0, 1

x is _______________.

When x is positive, 1

x is _______________. When x is negative,

1

x is

_______________.

When x becomes large, 1

x _______________. When x approaches 0,

1

x

_______________.

Steps: 1. Vertical Asymptotes 2. Signs 3. Invariant & Other Important Points

2. Given y f x , as shown, graph 1

yf x

.

3. Given 21f x x , graph y f x and

1y

f x.

4. Given y f x , as shown, graph 1

yf x

.

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

5. Given 1

22

f x x , graph y f x and 1

yf x

.

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

yf x

.