The given expression is:

$f(x) = \frac{1}{1 + e^{-(x + 10)}}$

This is a form of the sigmoid function, which is commonly used in fields like machine learning and statistics. Specifically, it takes the form:

$f(x) = \frac{1}{1 + e^{-z}}$

where $z = x + 10$ in this case.

The sigmoid function is often used because it outputs values between 0 and 1, which can be interpreted as probabilities in certain contexts. Here's a breakdown of the key properties of this function:

1. Range:

The output of the sigmoid function is always between 0 and 1, no matter the input value of $x$.

2. Asymptotes:

• As $x \to -\infty$, $f(x) \to 0$.
• As $x \to +\infty$, $f(x) \to 1$.

3. Inflection Point:

The function has an inflection point at $x = -10$, which is where the function transitions from increasing slowly to increasing rapidly.

Would you like further details, such as the derivative or applications of this function?

Here are some related questions to explore:

1. What is the derivative of the sigmoid function?
2. How is the sigmoid function applied in logistic regression?
3. What are the key differences between a sigmoid and a hyperbolic tangent (tanh) function?
4. How does adding a constant, like 10, affect the shape and shift of the sigmoid function?
5. What is the relationship between the sigmoid function and neural networks?

Tip: The sigmoid function is often replaced by the ReLU function in deep learning because ReLU mitigates the vanishing gradient problem.