Final answer:
To graph the function f(x) = e^x / x^3, start by identifying key points. Remember that the function is undefined at x = 0. As x approaches 0, the function approaches positive infinity. Also, the function is always positive and approaches 0 as x increases.
Step-by-step explanation:
To graph the function f(x) = e^x / x^3, we can start by identifying some key points on the graph.
When x = 0, the function is undefined because we cannot divide by zero. However, as x approaches 0 from the right side, the function approaches positive infinity. So, we can assign a point (0, +∞) to represent this behavior.
When x > 0, the function is always positive. As x increases, the function gets closer to 0. We can also identify a maximum point on the graph, which occurs when x is a small positive value. Let's say when x = 0.01, f(x) is approximately 1000. So, we can assign a point (0.01, 1000) to represent this maximum.
With these key points, we can sketch the graph of f(x) in an appropriate viewing rectangle.