each of these functions grows as x gets larger and larger. which function eventually exceeds the…

each of these functions grows as x gets larger and larger. which function eventually exceeds the others?\n$f(x)=\frac{3}{2}x$\n$g(x)=2^{x}-4$\n$h(x)=\frac{1}{2}x^{2}$

each of these functions grows as x gets larger and larger. which function eventually exceeds the others?\n$f(x)=\frac{3}{2}x$\n$g(x)=2^{x}-4$\n$h(x)=\frac{1}{2}x^{2}$

Answer

Explanation:

Step1: Recall growth - rate of functions

Exponential functions grow faster than polynomial functions, and linear functions are polynomial functions of degree 1.

Step2: Identify function types

$f(x)=\frac{3}{2}x$ is a linear function (a polynomial of degree 1). $h(x)=\frac{1}{2}x^{2}$ is a quadratic function (a polynomial of degree 2). $g(x)=2^{x}-4$ is an exponential function.

Step3: Compare growth - rates

As $x$ gets larger and larger, exponential functions grow faster than polynomial functions. Among the given functions, the exponential function $g(x)=2^{x}-4$ will eventually exceed the other two functions.

Answer:

$g(x)=2^{x}-4$