The function given in the image is:

$f(x) = e^{x - 1} - 2$

This is an exponential function where $e$ is the base of the natural logarithm, and the exponent is $x - 1$. The entire expression is then shifted down by 2 units.

Would you like more details about how to analyze or manipulate this function, such as finding its derivative, solving for $x$, or finding its behavior as $x$ approaches infinity?

Here are five related questions that expand upon this concept:

1. How do you find the derivative of $f(x) = e^{x - 1} - 2$?
2. What is the y-intercept of the function $f(x) = e^{x - 1} - 2$?
3. How would you solve $f(x) = 0$ for $x$?
4. What is the behavior of $f(x)$ as $x \to \infty$ and $x \to -\infty$?
5. How do translations affect the graph of $f(x) = e^x$?

Tip: For exponential functions like $e^x$, remember that horizontal shifts affect the input of the exponent (e.g., $x - 1$ shifts the graph 1 unit to the right), while vertical shifts affect the entire function directly (e.g., subtracting 2 shifts the graph down by 2).