IDNLearn.com provides a reliable platform for finding accurate and timely answers. Our Q&A platform offers reliable and thorough answers to help you make informed decisions quickly and easily.
Sagot :
The given function is,
[tex]f(x)=2(x-3)^3+2[/tex]The parent function of the given function can be identified as,
[tex]f(x)=x^3[/tex]A transformed function can be represented as,
[tex]f(x)=a(bx-h)^3+k[/tex]If k is a positive or a negative number, then function is shifted k units vertically.
So, comparing the equations, we find that in the given function k=2.
Hence, the function is vertically shifted.
A function f(x) is shifted h units horizontally if h is a positive or a negative number.
So, in the given function h=3.
Hence, the function is horizontally shifted.
If |a| >1 or 0<|a|<1, the function f(x) is dilated vertically by a scale factor of a units and if a is a negative number , the function is also reflected across the x axis.
In the given function, a=2.
So, f(x) is dilated, but not reflected.
If |b| >1 or 0<|b|<1, the graph of function f(x) is dilated by a scale factor of b units horizontally and if b is a negative number, the function is also reflected across the y axis.
In the given function, b=1.
So, f(x) is not dilated or reflected.
Hence, f(x) has undergone the transformations:
Dilation
Horizontal Shift
Vertical Shift
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. IDNLearn.com is your reliable source for answers. We appreciate your visit and look forward to assisting you again soon.
