Each of these functions grows as x gets larger and larger. Which function eventually exceeds the others? f(x)=(3)/(2)x g(x)=2^x-4 h(x)=(1)/(2)x^2

To determine which function eventually exceeds the others as x gets larger and larger, we need to analyze the behavior of each function.Let's start with the function f(x) = (3/2)x. This is a linear function with a positive slope of 3/2. As x increases, the value of f(x) will also increase at rate.Next, let's consider the function g(x) = 2^x - 4. This is an exponential function with a base of 2. As x increases, the value of g(x) will grow exponentially. However, there is a constant term of -4 that shifts the graph downward by 4 units.Finally, let's look at the function h(x) = (1/2)x^2. This is a quadratic function with a positive coefficient of 1/2. As x increases, the value of h(x) will grow at a quadratic rate.Comparing the three functions, we can see that the exponential function g(x) = 2^x - 4 will eventually exceed the other two functions as x gets larger and larger. This is because exponential growth is much faster than linear or quadratic growth.Therefore, the function that eventually exceeds the others is g(x) = 2^x - 4.