Subjects calculus

Function Decreasing F1C433

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** We need to determine the domain on which the given function is decreasing based on the graph description. 2. **Understanding decreasing functions:** A function is decreasing on intervals where the function values go down as $x$ increases. In other words, if $f(x_1) > f(x_2)$ for $x_1 < x_2$, the function is decreasing on that interval. 3. **Analyze the graph description:** The curve starts around $y=140$ at $x=0$, rises to a peak near $x=4$ with $y$ close to $190$, then decreases sharply, falling to near $y=0$ around $x=12$. 4. **Identify the decreasing interval:** Since the function rises until $x=4$ and then falls, the function is decreasing for $x > 4$ until about $x=12$ (where it approaches $y=0$). 5. **Conclusion:** The function is decreasing on the interval $$\boxed{(4, 12)}$$. This interval represents the domain where the function's output values decrease as $x$ increases.