which of the statements is true?\noa. as x approaches positive infinity, h(x) exceeds f(x) and g(x).\nob. as…

Explanation:

Step1: Analyze the behavior of (h(x))

Looking at the graph, (h(x)) is a linear function with a negative slope. As (x\to+\infty), (h(x)\to-\infty).

Step2: Analyze the behavior of (f(x))

(f(x)) is an exponential - like function (increasing but at a slower rate compared to a quadratic). As (x\to+\infty), (f(x)) increases, but its growth rate is less than that of a quadratic function.

Step3: Analyze the behavior of (g(x))

(g(x)) is a quadratic function (y = ax^{2}+bx + c) (in this case, (a>0)). For a quadratic function (y = ax^{2}+bx + c) with (a>0), as (x\to+\infty), (y = g(x)\to+\infty) and (g(x)) grows faster than a linear function (since the degree of a quadratic function (n = 2) and the degree of a linear function (m=1) and for large (x), (ax^{n}) dominates (bx^{m}) when (n>m)) and also faster than an exponential - like function (in the long - run, for (y = ax^{2}) and (y = b\cdot k^{x}) with (a,b,k>0,k\neq1), the quadratic will be overtaken by the exponential for very large (x) if (k > 1), but in the context of common basic functions, among linear (y=mx + b), quadratic (y = ax^{2}+bx + c(a>0)) and a non - linear increasing function (y = f(x)) (not exponential here), the quadratic will out - grow the linear and the non - linear (non - exponential) function).

Since (h(x)\to-\infty) as (x\to+\infty), and (g(x)) grows faster than (f(x)) as (x\to+\infty) (quadratic growth rate is higher than the non - exponential non - quadratic growth rate in the graph shown).

Answer:

D. As (x) approaches positive infinity, (g(x)) exceeds (f(x)) and (h(x))