Use what you know about translations of functions to analyze the graph of the function \( f(x)=(0.5)^{x-5}+8 \). You may wish to graph it and its parent function, \( y=0.5^{x} \), on the same axes. The parent function \( y=0.5^{x} \) is The function, \( f \), shifts the parent function 8 units across its domain because its base, \( b \), is such that \( \square \vee \). The function, \( f \), shifts the parent function 5 units

The parent function \( y=0.5^{x} \) is an exponential decay graph that decreases rapidly as \( x \) increases; it approaches the x-axis but never touches it, creating a horizontal asymptote at \( y=0 \). When you graph \( f(x)=(0.5)^{x-5}+8 \), you’ll see that it starts from the same shape as the parent function but is vertically transformed. The function \( f \) shifts the parent function up by 8 units because of the addition of 8, meaning that instead of approaching 0, it approaches 8. Additionally, there's a horizontal shift to the right by 5 units due to the expression \( x-5 \), moving everything over on the x-axis. So, while the original function decreases from a height of 1, the transformed version starts from 9 and has a similar decay characteristic, just floating 8 units above the x-axis!