The document discusses properties of graphs of reciprocal functions of the form y = 1/x. It notes that: 1) The graph can first be sketched by noticing it is undefined at x = 0, forming a vertical asymptote there. 2) As x approaches positive or negative infinity, the intercepts become asymptotes as well. 3) The graph is decreasing where x is positive and increasing where x is negative, with the reciprocal property.

1. (G) Graphs of Reciprocal
Functions
 
 
noticing;and
drawingfirstbysketchedbecan
1
ofgraphThe xfy
xf
y 

2. (G) Graphs of Reciprocal
Functions
 
 
noticing;and
drawingfirstbysketchedbecan
1
ofgraphThe xfy
xf
y 
 
 
 existsasymptoteverticalai.e.undefined,is
1
then,0when
xf
xf 

3. y
x
1
-1
 xfy 

4. y
x
1
-1
 xfy 

5. (G) Graphs of Reciprocal
Functions
 
 
noticing;and
drawingfirstbysketchedbecan
1
ofgraphThe xfy
xf
y 
 
 
 existsasymptoteverticalai.e.undefined,is
1
then,0when
xf
xf 
 
 
 interceptsbecomeasymptotesi.e.0,
1
then,when x
xf
xf 

6. y
x
1
-1
 xfy 

7. y
x
1
-1
 xfy 

8. y
x
1
-1
 xfy 

9. y
x
1
-1
 xfy 

10. (G) Graphs of Reciprocal
Functions
 
 
noticing;and
drawingfirstbysketchedbecan
1
ofgraphThe xfy
xf
y 
 
 
 existsasymptoteverticalai.e.undefined,is
1
then,0when
xf
xf 
 
 
 interceptsbecomeasymptotesi.e.0,
1
then,when x
xf
xf 
  versa-visaand,decreasingisreciprocalthe,increasingiswhen xf

11. (G) Graphs of Reciprocal
Functions
 
 
noticing;and
drawingfirstbysketchedbecan
1
ofgraphThe xfy
xf
y 
 
 
 existsasymptoteverticalai.e.undefined,is
1
then,0when
xf
xf 
 
 
 interceptsbecomeasymptotesi.e.0,
1
then,when x
xf
xf 
  versa-visaand,decreasingisreciprocalthe,increasingiswhen xf
 
 
etc.positive,is
1
positive,iswhen
xf
xf

12. y
x
1
-1
 xfy 

13. (G) Graphs of Reciprocal
Functions
 
 
noticing;and
drawingfirstbysketchedbecan
1
ofgraphThe xfy
xf
y 
 
 
 existsasymptoteverticalai.e.undefined,is
1
then,0when
xf
xf 
 
 
 interceptsbecomeasymptotesi.e.0,
1
then,when x
xf
xf 
  versa-visaand,decreasingisreciprocalthe,increasingiswhen xf
 
 
etc.positive,is
1
positive,iswhen
xf
xf
 
 
  
.reciprocalitsofpointsstationaryarecurveoriginal
theofpointsstationaryhence,is
1
ofderivativethe 2
xf
xf-
xf



14. y
x
1
-1
 xfy 

15. y
x
1
-1
 xfy 
 xf
y
1


16. y
x
1
-1
 xf
y
1
