This is a multi-part item. Consider the transformation \( f(x)=2^{x-h} \), for positive values of \( h \). Using graphing technology, graph \( f(x)=2^{x}, f(x)=2^{x-1} \), and \( f(x)=2^{x-2} \) and determine which statement is true. \begin{tabular}{l}\( f(x)=2^{x-h} \), for \( h>0 \), \\ will shift the graph down. \\ will shift the graph right. \\ \( \begin{array}{l}f(x)=2^{x-h}, \\ \text { will shift the graph left. } \\ \text { will shift the graph up. }\end{array} \) \\ \hline\end{tabular}

When you graph the functions \( f(x)=2^{x} \), \( f(x)=2^{x-1} \), and \( f(x)=2^{x-2} \), you will notice that each shift corresponds to moving the graph horizontally. The transformation \( f(x)=2^{x-h} \) actually shifts the graph to the right by \( h \) units. So, as \( h \) increases, the entire graph moves to the right along the x-axis. To visualize this, think of the standard function \( f(x) = 2^x \) starting at (0,1). When you look at \( f(x)=2^{x-1} \), it has the same shape but starts at (1,1), and \( f(x)=2^{x-2} \) starts at (2,1). Thus, the horizontal shift is clear, and the correct statement is that \( f(x)=2^{x-h} \) will shift the graph to the right.