The document discusses how to sketch the graph of a reciprocal function y = 1/f(x). Key steps include: 1) First sketch the graph of y = f(x); 2) Note that when f(x) = 0 there is a vertical asymptote, and when f(x) approaches infinity the asymptotes become x-intercepts; 3) The reciprocal graph is decreasing where the original is increasing, and vice versa.

1. (G) Graphs of Reciprocal
1
Functions
The graph of y  can be sketched by first drawing y  f  x 
f x
and noticing;

2. (G) Graphs of Reciprocal
1
Functions
The graph of y  can be sketched by first drawing y  f  x 
f x
and noticing;
1
 when f  x   0, then is undefined, i.e. a vertical asymptote exists 
f x

3. y  f x y
1
x
-1

4. y  f x y
1
x
-1

5. (G) Graphs of Reciprocal
1
Functions
The graph of y  can be sketched by first drawing y  f  x 
f x
and noticing;
1
 when f  x   0, then is undefined, i.e. a vertical asymptote exists 
f x
1
 when f  x   , then  0, i.e. asymptotes become x intercepts 
f x

6. y  f x y
1
x
-1

7. y  f x y
1
x
-1

8. y  f x y
1
x
-1

9. y  f x y
1
x
-1

10. (G) Graphs of Reciprocal
1
Functions
The graph of y  can be sketched by first drawing y  f  x 
f x
and noticing;
1
 when f  x   0, then is undefined, i.e. a vertical asymptote exists 
f x
1
 when f  x   , then  0, i.e. asymptotes become x intercepts 
f x
 when f  x  is increasing, the reciprocal is decreasing, and visa - versa

11. (G) Graphs of Reciprocal
1
Functions
The graph of y  can be sketched by first drawing y  f  x 
f x
and noticing;
1
 when f  x   0, then is undefined, i.e. a vertical asymptote exists 
f x
1
 when f  x   , then  0, i.e. asymptotes become x intercepts 
f x
 when f  x  is increasing, the reciprocal is decreasing, and visa - versa
1
 when f  x  is positive, is positive, etc.
f x

12. y  f x y
1
x
-1

13. (G) Graphs of Reciprocal
1
Functions
The graph of y  can be sketched by first drawing y  f  x 
f x
and noticing;
1
 when f  x   0, then is undefined, i.e. a vertical asymptote exists 
f x
1
 when f  x   , then  0, i.e. asymptotes become x intercepts 
f x
 when f  x  is increasing, the reciprocal is decreasing, and visa - versa
1
 when f  x  is positive, is positive, etc.
f x
1 -f  x 
 the derivative of is , hence stationary points of the
f  x   f  x  2
original curve are stationary points of its reciprocal.

14. y  f x y
1
x
-1

15. y  f x y
1
y
f x
1
x
-1

16. y
1
y
f x
1
x
-1