Question

The functions f and g are defined by fx=8x+33 and gx=2. 1.2x 1

Which function eventually grows faster, f or g? explain how you know.
80 points

Answer 1

To determine which function eventually grows faster, we need to look at their growth rates as x approaches infinity.

For function f(x), the growth rate is 8x, which means that as x gets larger, f(x) gets larger at a rate of 8 times x.

For function g(x), the growth rate is 1.2x, which means that as x gets larger, g(x) gets larger at a rate of 1.2 times x.

Since 8x grows faster than 1.2x as x approaches infinity, we can conclude that function f(x) grows faster than function g(x) in the long run.

Therefore, function f(x) eventually outgrows function g(x).