1. The problem asks to write a function for the graph related to $f(x) = 5^x$ where the graph is vertically shifted upwards by a constant $k$. 2. The general form for vertical shifts of a function $f(x)$ is: $$g(x) = f(x) + k$$ where $k$ is a constant that shifts the graph up if positive, or down if negative. 3. Since $f(x) = 5^x$, the function $g(x)$ becomes: $$g(x) = 5^x + k$$ 4. This means the entire graph of $5^x$ moves up by $k$ units. 5. The graph still passes above the x-axis and rises steeply as $x$ increases, but the y-values are increased by $k$. Final answer: $$g(x) = 5^x + k$$