Question

Which of the following statements is true about the functions f(x) and g(x) shown?

Answer 1

The rate of change of the function g(x) will eventually be greater than the rate of change of the functon f(x)

Here, we want to select the correct options about the two given functions

As we can see, the function f(x) is linear, while g(x) is exponential

While we can get the rate of change of linear function as constant, the rate of change of an exponential function is not constant and as such, we cannot determine the rate of change of an exponential function for all the points in the function

So what this mean is that we can only have the rate of change for a particular range if we are determining the rate of change for an exponential function which of course will be different for another set of range

Now, looking at the plot, at the initial stage, the rate of change of g(x) is less than that of f(x); at the later stage, towards the top, the rate of change of g(x) is greaterbthan that of f(x)

So conslusively;

The rate of change of the function g(x) will eventually be greater than the rate of change of the functon f(x)