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).

Answer 1

An exponential function of the form y = -A b^x fits. The horizontal asymptote y = 0 and the point (0,−2) give A = 2 and the negative sign, so y = -2 b^x. Using (1,−5) gives −2 b = −5 → b = 2.5.

Thus the graph is y = −2(2.5)^x (equivalently y = −2 e^{(ln 2.5)x}).