To answer the questions based on the information provided in the image:

1. Growth Factor (Common Ratio): The function given is $f(x) = 3 \cdot 4^x$. In this exponential function, the base of the exponent, $4$, represents the growth factor or common ratio. Therefore, the growth factor is 4.

2. Range of the Function: The graph of $f(x) = 3 \cdot 4^x$ shows an exponential growth, where all values are above the x-axis. This means that the range of $f(x)$ is entirely positive. So, the correct choice to complete the sentence is:

   • "The graph shows that the range values for $f(x) = 3 \cdot 4^x$ are all positive."

Would you like a deeper explanation of exponential functions or the characteristics of their graphs?

Here are five questions to consider:

1. What are the main differences between exponential growth and exponential decay?
2. How does changing the base in an exponential function affect the graph?
3. What happens to the function $f(x) = 3 \cdot 4^x$ if we change the coefficient from 3 to another positive value?
4. How can we determine the asymptote of an exponential function like $f(x) = 3 \cdot 4^x$?
5. What are real-life examples of exponential growth and decay?

Tip: When analyzing exponential functions, always check the base of the exponent to determine if the function represents growth (base > 1) or decay (0 < base < 1).