which function increases at a faster rate on 0 to infinity, f(x) = x2 or g(x) = 2x? explain your reasoning

Using a table of values, the outputs of f(x) for whole numbers are 0, 1, 4, 9, 16, 25, 36, and so on. For the same input values, g(x) has outputs of 1, 2, 4, 8, 16, 32, and 64. Continuing to double the output each time results in larger outputs than those of f(x). The exponential function, g(x), has a constant multiplicative rate of change and will increase at a faster rate than the quadratic function.

Step-by-step explanation:

MrRoyal MrRoyal · Answer 2 · 2022-05-18T11:34:00+02:00

The function that increases at a faster rate on 0 to infinity is g(x) = 2ˣ

How to determine the function with faster rate?

The functions are given as:

f(x) = x² --- quadratic

g(x) = 2ˣ --- exponential

The exponential function has the same base as the power of the quadratic function.

This means that the exponential function would increase faster from the point where f(x) = g(x)

This is illustrated using the following table

x 0 1 2 3 4 5

f(x) 0 1 4 9 16 25

g(x) 1 2 4 8 16 32

Hence, the function that increases at a faster rate on 0 to infinity is g(x) = 2ˣ