1. Which of the following statements is true of the exponential function \( y=\frac{1}{3} \cdot 5^{x} \) ?

To analyze the exponential function \( y = \frac{1}{3} \cdot 5^{x} \), we can consider several properties of exponential functions. Here are some key points to evaluate: 1. **Growth Behavior**: Since the base \( 5 \) is greater than \( 1 \), the function will exhibit exponential growth as \( x \) increases. 2. **Y-Intercept**: The y-intercept occurs when \( x = 0 \): \[ y = \frac{1}{3} \cdot 5^{0} = \frac{1}{3} \cdot 1 = \frac{1}{3} \] 3. **Asymptotic Behavior**: As \( x \) approaches negative infinity, \( y \) approaches \( 0 \) but never actually reaches it. This indicates that the function has a horizontal asymptote at \( y = 0 \). 4. **Domain and Range**: - The domain of the function is all real numbers \( (-\infty, \infty) \). - The range is \( (0, \infty) \) since \( y \) is always positive. 5. **Increasing Function**: The function is increasing for all \( x \) because the derivative of an exponential function with a positive base is always positive. Based on these properties, we can conclude that the function \( y = \frac{1}{3} \cdot 5^{x} \) is an increasing function that approaches \( 0 \) as \( x \) decreases and has a y-intercept of \( \frac{1}{3} \). If you have specific statements to evaluate, please provide them, and I can determine which one is true based on the analysis above.