This document provides examples for graphing reciprocals of functions. It explains that for reciprocals, smaller numbers on the x-axis become larger on the y-axis, and vice versa. An example graphs the reciprocal of f(x)=1/x^2. It notes that reciprocals can be written in the form f(x)=k/x+h, where k and h are determined from the original function. Further examples graph the reciprocals of f(x)=2/x+4 and f(x)=sin(x).

1. Exercise #10
Graphing Reciprocals
x
Recall Graph a) f ( x)
x 2
3
b) f ( x) 2
x 4
12
c) f ( x) 2
x 4
To graph reciprocals, remember that the smaller numbers become large and the larger
numbers become small.
1
Ex. = _____ , where as 3 = _____
2
Example
1
Graph f ( x) x2 1 Now graph .
f ( x)
y y
x x
To graph the reciprocal, choose points and take the reciprocal of the y-coordinate.
1
f ( x) x y x y
f ( x)

2. What do you notice?
1.
2.
3.
4.
1
You may use the form f ( x) k where h =
x h
and k =
Example
1
Graph f ( x) 2 x 1 Graph
f ( x)
y y
x x
Example
1
Graph f ( x) sin x Graph
f ( x)
y y
x x

3. Example
1
If this is the graph of f ( x) , graph .
f ( x)
y y
x x