Question

n the graph below, f(x) is a linear function, and g(x) is an exponential function.



image.png

Which statement BEST explains the behavior of the graphs of the functions as x increases?


g(x) eventually exceeds f(x) because the rate of change of f(x) increases as x increases, whereas the rate of change of g(x) is constant.


g(x) eventually exceeds f(x) because the rate of change of g(x) increases as x increases, whereas the rate of change of f(x) is constant.


f(x) eventually exceeds g(x) because the rate of change of g(x) decreases as x increases, whereas the rate of change of f(x) is constant.


f(x) eventually exceeds g(x) because the rate of change of f(x) decreases as x increases, whereas the rate of change of g(x) is constant.

Answer 1

g(x) eventually exceeds f(x) because the rate of change of g(x) increases as x increases, whereas the rate of change of f(x) is constant.

(Linear f has constant slope; exponential g has an increasing derivative so it eventually outgrows any line.)