Question

In the graph below, f(x) is a linear function, and g(x) is an exponential function. Which statement best explains the behavior of the graphs of the functions as x increases?

Answer 1

Given:

The graphs of f(x) and g(x)

Let us describe the behavior of f(x) and g(x) individually

Behavior of f(x)

f(x) is a straight-line graph. The rate of change of f(x) is constant

Behavior of g(x)

g(x) is the graph of an exponential function. The value of g(x) rises exponentially as x increases.

Combining the behavior of f(x) and g(x)

Since g(x) rises exponentially as x increases, it would eventually exceed f(x)

Answer:

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. (Option B)