Minimum value of f(x) = |0| - 4 = -4
Maximum is +infinity.
Therefore the range of f(x) is [-4,+infinity).
And the graph looks like this: https://www.desmos.com/calculator/y2wyt5oh1u
g(x) = x^2 + 2x - 3 = (x+1)^2 - 4
Min value of g(x) also equals -4, and max value is also +infinity.
Therefore g(x) is one of the answers.
k(x) = sqrt(x) - 4.
Min value = sqrt(0) - 4 = -4
Max value is also +infinity.
Therefore k(x) is the other answer.
And the graphs of g(x) and k(x) look like this: https://www.desmos.com/calculator/sjurr0goyx