how does the value of k affect the graph of f(x)=2^x+k
The value of k in the function f(x) = 2^x + k determines the vertical shift of the graph.
When k > 0, the graph of the function will be shifted upward by |k| units, as every y-value will be increased by k. This means that the graph will be above the original graph of f(x) = 2^x.
When k < 0, the graph of the function will be shifted downward by |k| units, as every y-value will be decreased by k. This means that the graph will be below the original graph of f(x) = 2^x.
If k = 0, then the graph of the function will be the same as the original graph of f(x) = 2^x, with no vertical shift.
In summary, the value of k affects the graph of f(x) = 2^x + k by shifting the graph either upward or downward depending on whether k is positive or negative, respectively.