x2 t07 04 reciprocal functions (2011)

(G) Graphs of Reciprocal Functions

noticing; and

drawingfirst by sketched becan 1 ofgraph The xfyxf

y

(G) Graphs of Reciprocal Functions

noticing; and

drawingfirst by sketched becan 1 ofgraph The xfyxf

y

exists asymptote verticala i.e. undefined, is 1 then ,0 when xf

xf

y

x

1

-1

xfy

y

x

1

-1

xfy

(G) Graphs of Reciprocal Functions

noticing; and

drawingfirst by sketched becan 1 ofgraph The xfyxf

y

exists asymptote verticala i.e. undefined, is 1 then ,0 when xf

xf

intercepts become asymptotes i.e. 0,1 then , when xxf

xf

y

x

1

-1

xfy

y

x

1

-1

xfy

y

x

1

-1

xfy

y

x

1

-1

xfy

(G) Graphs of Reciprocal Functions

noticing; and

drawingfirst by sketched becan 1 ofgraph The xfyxf

y

exists asymptote verticala i.e. undefined, is 1 then ,0 when xf

xf

intercepts become asymptotes i.e. 0,1 then , when xxf

xf

versa-visaand,decreasing isreciprocalthe,increasing is when xf

(G) Graphs of Reciprocal Functions

noticing; and

drawingfirst by sketched becan 1 ofgraph The xfyxf

y

exists asymptote verticala i.e. undefined, is 1 then ,0 when xf

xf

intercepts become asymptotes i.e. 0,1 then , when xxf

xf

versa-visaand,decreasing isreciprocalthe,increasing is when xf

etc. positive, is 1 positive, is when xf

xf

y

x

1

-1

xfy

(G) Graphs of Reciprocal Functions

noticing; and

drawingfirst by sketched becan 1 ofgraph The xfyxf

y

exists asymptote verticala i.e. undefined, is 1 then ,0 when xf

xf

intercepts become asymptotes i.e. 0,1 then , when xxf

xf

versa-visaand,decreasing isreciprocalthe,increasing is when xf

etc. positive, is 1 positive, is when xf

xf

.reciprocal its of points stationary are curve original

theof points stationary hence , is 1 of derivative the 2xfxf-

xf

y

x

1

-1

xfy

y

x

1

-1

xfy

xfy 1

y

x

1

-1

xfy 1