Question

Which function is represented by the graph below?

On a coordinate plane, a curve opens left and down in quadrants 3 and 4. The curve approaches the negative x-axis as an asymptote in quadrant 3, curves down, going through (0, negative 2) and decreases more and more rapidly in quadrant 4 passing near (1, negative 5).
f(x)=e-2x
f(x)=-2 in(x)
f(x)=-in(2x)
f(x)=-2ex

Answer 1

f(x) = -2e^x.

Reason: f(0) = -2 fits only -2e^x. As x → −∞, -2e^x → 0− so the x‑axis is a horizontal asymptote approached from below, and as x increases the function decreases rapidly (f(1) = -2e ≈ -5.44, near (1, −5)). Logarithmic options have domain x>0 and don't match the left‑side behavior.