The graph of the f(x) is show below. Graph each transformed function and list in words the transformation used?

enter image source here
I'm kind of confused on how to shift the graphs. I do know that you use this formula
y=A+(B(x−h))+k
to graph these functions.

1 Answer
Brandon Y.
Nov 29, 2017

This is the original graph of #f(x)#.

enter image source here

a) This is the graph of #g(x)=f(-x)+1#.
enter image source here

b) This is the graph of #h(x)=-1/2f(x)-2#.
enter image source here

c) This is the graph of #k(x)=2f(x+3)-1#.
enter image source here

Explanation:

Use this equation to solve algebraically: #y=af(b(x-h))+k#.

For the graph of #g(x)=f(-x)+1#, there is a reflection in the #y#-axis and a vertical translation 1 unit up. In other words, #b# is negative, and #k = 1#.

#(x,y)# on #y=f(x)# will be #(-x,y+1)# on #g(x)=f(-x)+1#.

#(-1,4) ->(1,5)#
#(1,0) ->(-1,1)#
#(3,4)->(-3,5)#

For the graph of #h(x)=-1/2f(x)-2#, there is a reflection in the #x#-axis, a vertical compression by a factor of 1/2, and a vertical translation of 2 units down. In other words, #a=-1/2#, and #k=-2#.

#(x,y)# on #y=f(x)# will be #(x,1/2y-2)# on #h(x)=-1/2f(x)-2#.
#(-1,4) ->(-1,-4)#
#(1,0) ->(1,-2)#
#(3,4)->(3,-4)#

For the graph of #k(x)=2f(x+3)-1#, there is a vertical stretch by a factor of 2, a horizontal translation 3 units left, and a vertical translation 1 unit down. In other words, #a=2#, #h=-3#, and #k=-1#.

#(x,y)# on #y=f(x)# will be #(x-3,2y-1)# on #k(x)=2f(x+3)-1#.

#(-1,4) ->(-4,7)#
#(1,0) ->(-2,-1)#
#(3,4)->(0,7)#

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