Consider the graphs of linear function f(x) = 3x, quadratic function g(x) = 3x2, and exponential function h(x) = 2x. Which statement about the functions f, g, and h is correct?

Question

A. As x increases, the value of f(x) will eventually exceed the values of g(x) and h(x).

B. As x increases, the value of g(x) will eventually exceed the values of f(x) and h(x).

C. As x increases, the value of h(x) will eventually exceed the values of f(x) and g(x).

D. As x increases, the values of both f(x) and g(x) will eventually exceed the value of h(x

Answer 1

This problem has to do with the relative "strengths" of functions. I'd recommend you try plugging in x values for each of the equations to see how the behaviors differ.

For example:

x = 1:

1. f(1) = 3
2. g(1) = 3
3. h(1) = 2

x = 10:

1. f(10) = 30
2. g(10) = 300
3. h(10) = 1024

x = 100:

1. f(100) = 300
2. g(100) = 30,000
3. h(100) = 1.27 x 10^30

What do these answers tell you about the behaviors of the three different equations?