Question

Based on the graph of the functions, which of the following statements is true?

A.
f(x) eventually exceeds g(x) because f(x) is increasing linearly
B.
At x = 13, the value of f(x) is more than the value of g(x).
C.
g(x) eventually exceeds f(x) because g(x) is increasing exponentially
D.
Over the interval [3, 5], the average rate of change of g is greater than the average rate of change of f.

Answer 1

Answer:

  C.  g(x) eventually exceeds f(x) because g(x) is increasing exponentially

Step-by-step explanation:

Comments on the other choices:

  A -- an exponential function eventually exceeds any polynomial function. (A linear function is a polynomial of degree 1.)

  B -- at x=13, f(x) = 17; g(x) ≈ 18.2, so g(x) is more

  D -- over the given interval, the average rate of change of g(x) is about 1/2 (1 unit rise for 2 units run) compared to the slope of 1 that f(x) has.