1. The problem asks us to determine the interval on which the function $f(x) = e^x$ is increasing. 2. Recall that $f(x) = e^x$ is an exponential function where the base $e$ is Euler's number, which is approximately 2.718. 3. The derivative of $f(x)$ is $f'(x) = e^x$. 4. Since $e^x > 0$ for all real numbers $x \in \mathbb{R}$, the derivative is always positive. 5. A function with a positive derivative on an interval is increasing on that interval. 6. Therefore, $f(x)=e^x$ is increasing on the entire real line, $\mathbb{R}$. 7. Among the given options: - A) $]0, \infty[$ is only positive real numbers, - B) $\mathbb{R}$ is all real numbers, - C) $]-\infty,0]$ is all negative real numbers including zero, - D) $]1, \infty[$ is all real numbers greater than 1. 8. Since the function is increasing everywhere, the correct answer is B) $\mathbb{R}$. Final answer: The function $f(x)=e^x$ is increasing on the interval $\boxed{\mathbb{R}}$.