BRAINLIEST TO BESTWhich function grows at the fastest rate for increasing values of x? A) f(x)=12x^2+4x B) h(x)=4^x C) g(x)=100x D) p(x)=3x3+1

First of all, let's study each function:

Function A) 

[tex]f(x)=12x^2+4x[/tex]

This is a quadratic function. This type of function is a second-degree polynomial function.

Function B) 

[tex]h(x)=4^x[/tex]

This is an exponential function. This type of function is a non-algebraic function. It's also called transcendental function.

Function C)

[tex]g(x)=100x[/tex]

It's a straight line with slope equal to 100 and without y-intercept.

Function D)

[tex]p(x)=3x^3+1[/tex]

It's a cubic function. It's a third-degree polynomial function.

So from the figure it is obvious that the function that grows at the fastest rate is the exponential function B). In fact, an exponential function always grows more quickly than a polynomial function.