Which of the following describe the correct transformations of \( f(x)=2^{x-1}+3 \) from \( f(x)=2^{x} \) ? Select all that apply. The graph of \( f(x) \) is shifted to the right 1 unit. The graph of \( f(x) \) is reflected over the \( x \)-axis. The graph of \( f(x) \) is shifted up 3 units. The graph of \( f(x) \) is shifted down 3 units. The graph of \( f(x) \) is shifted to the left 1 unit.

The transformations of \( f(x)=2^{x-1}+3 \) from \( f(x)=2^{x} \) involve two key shifts. First, the expression \( x-1 \) indicates a shift of the graph to the right by 1 unit. Second, the addition of 3 translates the entire graph upwards by 3 units. So, the correct transformations are: the graph of \( f(x) \) is shifted to the right 1 unit and the graph of \( f(x) \) is shifted up 3 units—you've got a double whammy of moves here! For a little extra insight, remember that the basic graph of \( 2^x \) is an increasing curve that approaches but never touches the x-axis. Any adjustments you make, such as shifts, will retain the essential shape of the exponential curve; it’s just on the move! Reviewing transformations can help visualize functions better too!