The graph shown in the image matches the function $f(x) = e^x$, which is an exponential growth curve. Here's why:

1. The curve increases exponentially as $x$ becomes larger.
2. It passes through the point $(0,1)$, consistent with $f(x) = e^x$.
3. The curve remains strictly positive for all $x$, never crossing or touching the $x$-axis.

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Here are five related questions to explore:

1. What are the key characteristics of exponential functions like $f(x) = e^x$?
2. How do you determine if a function is linear, quadratic, or exponential from a graph?
3. What transformations can be applied to $f(x) = e^x$, and how would they affect the graph?
4. How does the graph of $f(x) = e^x$ compare to that of $f(x) = 2^x$?
5. How can you identify the equation of a graph if it’s not one of the standard functions?

Tip: Exponential functions have unique properties, such as a rapid rate of increase or decrease, making them easy to recognize graphically.