Which statements describe the function \( f(x)=3\left(\frac{1}{3}\right)^{x} \) ? Check all that apply. Each successive output is the previous output divided by 3 . As the domain values increase, the range values decrease. The graph of the function is linear, decreasing from left to right. Each successive output is the previous output multiplied by 3 . The range of the function is all real numbers greater than 0 . The domain of the function is all real numbers greater than 0 .

Let's analyze the function \( f(x) = 3\left(\frac{1}{3}\right)^x \): 1. **Successive Outputs:** - For each increase in \( x \) by 1, the function becomes: \[ f(x+1) = 3\left(\frac{1}{3}\right)^{x+1} = 3\left(\frac{1}{3}\right)^x \cdot \frac{1}{3} = \frac{f(x)}{3} \] This means each successive output is the previous output **divided by 3**. 2. **Behavior as \( x \) Increases:** - Since the base \( \frac{1}{3} \) is less than 1, the function decreases as \( x \) increases. Therefore, as the domain values increase, the range values **decrease**. 3. **Graph Characteristics:** - The function is **exponential**, not linear. It decreases from left to right but is not a straight line. 4. **Range and Domain:** - **Range:** The function \( f(x) = 3\left(\frac{1}{3}\right)^x \) always yields positive values for any real \( x \). Therefore, the range is **all real numbers greater than 0**. - **Domain:** The domain of an exponential function includes all real numbers, not just those greater than 0. Based on this analysis, the correct statements are: - **Each successive output is the previous output divided by 3.** - **As the domain values increase, the range values decrease.** - **The range of the function is all real numbers greater than 0.** **Correct Options:** - Each successive output is the previous output divided by 3. - As the domain values increase, the range values decrease. - The range of the function is all real numbers greater than 0.