Answer:
We have the function, [tex]g(x)=x^{3}-x[/tex].
It can be seen that various transformations are applied to the function g(x) in order to obtain the new function.
As the new function is [tex]0.5g(x-2)+1[/tex] i.e. [tex]\frac{1}{2}g(x-2)+1[/tex]
We get that,
The function g(x) is translated to the right by 2 units, then g(x) ⇒ g(x-2).
Further, g(x-2) is shrinked vertically by [tex]\frac{1}{2}[/tex], which gives g(x-2) becomes [tex]\frac{1}{2}g(x-2)[/tex].
Finally, the function [tex]\frac{1}{2}g(x-2)[/tex] is translated 1 unit upwards, then [tex]\frac{1}{2}g(x-2)[/tex] ⇒ [tex]\frac{1}{2}g(x-2)+1[/tex]
Hence, the graph of the new function is given below.
