1. **Problem statement:** We need to identify which properties every exponential function satisfies, especially focusing on the natural exponential function $y = e^x$. 2. **Recall the definition:** An exponential function with base $a > 0$ and $a \neq 1$ is defined as $f(x) = a^x$. The natural exponential function uses base $e \approx 2.718281$. 3. **Properties of exponential functions:** - **Range:** Since $a^x > 0$ for all real $x$, the range is $\mathbb{R}^+ = (0, \infty)$. - **Boundedness:** Exponential functions are bounded from below by 0 but not bounded above. - **Injectivity:** Exponential functions are one-to-one (injective) because $a^x$ is strictly increasing if $a > 1$ and strictly decreasing if $0 < a < 1$. - **Monotonicity:** They are strictly monotone (either strictly increasing or strictly decreasing) over $\mathbb{R}$. 4. **Explanation:** - The function passes through $(0,1)$ because $a^0 = 1$. - The function never touches or crosses the x-axis, so it never takes zero or negative values. - The function's strict monotonicity ensures injectivity. 5. **Conclusion:** The correct properties are: - The range is $\mathbb{R}^+$ - Are bounded from below - Are injective - Are strictly monotone **Final answer:** All the given options are correct for every exponential function.