1. **State the problem:** We are analyzing the function's domain, range, horizontal asymptote, y-intercept, and end behavior based on the given graph description. 2. **Domain:** The domain is given as $(-\infty, \infty)$, meaning the function is defined for all real numbers. 3. **Horizontal asymptote:** The graph approaches 0 but remains positive as $x \to -\infty$, so the horizontal asymptote is $y=0$. 4. **Y-intercept:** The curve passes near the origin at approximately $(0,1)$, so the y-intercept is $f(0) = 1$. 5. **End behavior:** - As $x \to -\infty$, $f(x) \to 0^+$ (approaches zero from above). - As $x \to \infty$, $f(x) \to \infty$ (increases without bound). 6. **Range:** Since the function approaches 0 but stays positive and increases without bound, the range is $(0, \infty)$. 7. **Summary:** - Domain: $(-\infty, \infty)$ - Range: $(0, \infty)$ - Horizontal asymptote: $y=0$ - Y-intercept: $(0,1)$ - End behavior: $f(x) \to 0^+$ as $x \to -\infty$, $f(x) \to \infty$ as $x \to \infty$. This behavior is typical of an exponential growth function like $f(x) = e^x$.