Use what you know about translations of functions to analyze the graph of the function [tex]f(x)=(0.5)^{x-5}+8[/tex]. You may wish to graph it and its parent function, [tex]y=0.5^x[/tex], on the same axes.
The parent function [tex]y=0.5^x[/tex] is ______ across its domain because its base, b, is such that ______.
The function, f, shifts the parent function 8 units ______.
The function, f, shifts the parent function 5 units ______.
Answer (2)
The parent function y = 0. 5 x is decreasing because its base b = 0.5 is between 0 and 1.
The function f ( x ) shifts the parent function 8 units upward.
The function f ( x ) shifts the parent function 5 units to the right.
Therefore, the transformations are a vertical shift of 8 units up and a horizontal shift of 5 units to the right. $\boxed{decreasing, 0
The function f ( x ) = ( 0.5 ) x − 5 + 8 is derived from the parent function y = 0. 5 x which is decreasing due to a base of 0.5 . The function shifts the graph 8 units upward and 5 units to the right. This leads to a transformation where the new graph maintains a decrease but is positioned differently on the coordinate plane.
;
