The graph shown is an exponential function. Let's break down why this is the case based on the options provided:

• An exponential function with a growth factor of 2 is the correct choice. This is because the graph shows a consistent exponential growth, which matches the nature of exponential functions (e.g., $y = 2^x$). The curve gets steeper as $x$ increases, which is characteristic of exponential growth with a base greater than 1.

To eliminate the other options:

1. A quadratic equation with differences of 1, then 2, then 4, ...: Quadratic functions form parabolas (either opening upwards or downwards), and they do not exhibit exponential growth. This option does not describe an exponential curve.
2. A quadratic function with a constant difference of 2: Quadratic functions have a constant second difference in their y-values. The graph presented does not match this pattern.
3. An exponential function with growth factors of 1, then 2, then 4, ...: This option is close but not entirely accurate. The correct way to describe this growth is that the function doubles its output as $x$ increases, indicating a consistent growth factor rather than varying factors.

Thus, the best description of the graph is:

• An exponential function with a growth factor of 2.

Would you like more details on exponential functions, or do you have any other questions?

Here are some related questions for further exploration:

1. What is the general form of an exponential function?
2. How do you differentiate between quadratic and exponential functions based on their graphs?
3. What are the characteristics of exponential growth and decay?
4. How can you determine the growth rate of an exponential function from its graph?
5. What happens when the base of an exponential function is between 0 and 1?

Tip: Exponential functions grow faster than any polynomial function as $x$ increases.