1. The problem asks us to describe the behavior of the exponential function $g(x)$ as $x$ approaches infinity. 2. From the graph description, $g(x)$ is an exponentially decreasing function starting near $y=10$ at $x=-10$ and tending downward toward $y=0$ as $x$ increases. 3. Important rule: For exponential decay functions of the form $g(x) = a \cdot b^x$ where $0 < b < 1$, as $x \to \infty$, $g(x) \to 0$ but never actually reaches zero. 4. Therefore, as $x$ approaches infinity, the value of $g(x)$ approaches 0 but does not equal 0. 5. Among the options, the statement that best describes this behavior is: C. The value of $g(x)$ approaches 0. Final answer: C