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Shifting, Reflection, Etc.

graph y = ( x - 1 )^3 ... the disco graph! ... shift right to x = 1 ... ( 1 - 1 )^3 = ( 0 )^3

 

 

 

 

 

 

 

 

 

graph of y = ( x - 1 )^3 ... some points on the graph are ( 0 , -1 ) , ( 1 , 0 ) and ( 2 , 1 )

 

YOUR TURN:

Graph

y = -2x^3

 

Graph y = - sqrt( x ) ... Square Root Guy! ... up-side-down

 

 

 

graph of y = - sqrt( x ) ... some points on the graph are ( 1 , -1 ) and ( 4 , -2 )

 

Graph

    y = sqrt( x + 4 ) - 2 ... shift left four to x = -4 and down 2 ... sqrt( -4 + 4 ) = sqrt( 0 )

 

 

 

 

graph of y = sqrt( x + 4 ) - 2 ... some points on the graph are ( -4 , -2 ) and ( -3 , -1 )

 

TRY IT:

Graph

y = 3 sqrt( x ) - 1

 

Graph y = 1 / ( x - 2 ) ... it's 1/x guy! ... the shift is with the x ... shift right to x = 2 ... 1 / ( 2 - 2 ) = 1 / 0

 

 

graph of y = 1 / ( x - 2 ) ... asymptote at x = 2
 

This dashed line is called an asymptote.  Graphs approach, but they don't touch!

 

TRY IT:

Graph

y = 1 / ( x - 1 )^2