The function g(x) = 2^x. The function f(x) = 2^x + k and k < 0. Which of the following statements is
true?
The graph of f(x) is shifted k units to the left of the graph of g (x).
The graph of f(x) is shifted k units to the right of the graph of g (x).
The graph of f(x) is shifted k units above the graph of g(x).
The graph of f(x) is shifted k units below the graph of g (x).
show your work
The correct statement is: The graph of f(x) is shifted k units below the graph of g(x).
When we have f(x) = 2^x + k, the graph of f(x) is the same as the graph of g(x) = 2^x, but shifted vertically down by k units.
To see this, let's consider an example with k = -2. The graph of g(x) = 2^x is shown as a regular exponential function curve. When we add k = -2 to f(x), the graph of f(x) is shifted down by 2 units compared to g(x) at each point.
Therefore, the graph of f(x) = 2^x + k is shifted k units below the graph of g(x) = 2^x.