Question 1159886: a graph with the following points: (-6,0), (-3,3), (0,0), (1,-1), (3,-1). List the transformation in correct order that have taken place in graph of f in order to result in function P(x)= -f(3x)+1.
what operation do you apply to x coordinates of the key points of f in order to transform them into the new graph P(x)?
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
This is the graph of y = f(x)
First we form the graph of f(3x) which, since 3 is greater than 1, SHRINKS the
graph HORIZONTALLY by a factor of the reciprocal of 3. It doesn't affect the
y-values, but divides the x-coordinates by 3
(-6,0) --> (-2,0)
(-3,3) --> (-1,3)
(0,0) --> (0,0)
(1,-1) --> (-1/3,3)
(3,-1) --> (1,-1)
Here is the graph of y = f(3x):
Next we form the graph of -f(3x) which REFLECTS the graph across the x-axis. It
doesn't affect the x-values, but multiplies the y-coordinates by -1, which is to
say, it changes their signs.
(-2,0) --> (-2,0)
(-1,3) --> (-1,-3)
(0,0) --> (0,0)
(-1/3,-1) --> (-1/3,1)
(1/3,-1) --> (1/3,1)
finally we form the graph of y=-f(3x)+1 which SHIFTS the graph 1 unit upward. It
doesn't affect the x-values, but ADDS 1 to all the y-coordinates. We relabel
this final graph as P(x) = -f(3x)+1
(-2,0) --> (-2,1)
(-1,-3) --> (-1,-2)
(0,0) --> (0,1)
(-1/3,1) --> (-1/3,2)
(1/3,1) --> (1/3,2)
Edwin
|
|
|
