To identify each curve (blue, red, green) as the position, velocity, or acceleration function, we can use the relationships between these functions:

1. Position Function is the original function. Its derivative is the velocity function.
2. Velocity Function is the derivative of the position function, and its derivative is the acceleration function.
3. Acceleration Function is the derivative of the velocity function.

Looking at the graph:

• The green curve is increasing steadily, implying it represents a position function (its slope changes, so its derivative changes).
• The red curve starts positive, decreases, and then levels off, which suggests it is the velocity function (the rate of change of position).
• The blue curve oscillates and crosses the x-axis multiple times, behaving like an acceleration function since it appears to be the second derivative of the position function.

Answer:

1. Position Function: C (Green)
2. Velocity Function: B (Red)
3. Acceleration Function: A (Blue)

Would you like any further details on these relationships or the process of differentiation?

Here are 5 related questions you might want to explore:

1. How can you determine the velocity from the position function analytically?
2. What does it mean when the acceleration is negative or positive?
3. How can you calculate displacement from the velocity graph?
4. How do inflection points on the position graph relate to the velocity and acceleration?
5. What are some real-world examples of these types of functions in motion?

Tip: Remember that the slope of a function gives valuable information about its rate of change, whether it's position, velocity, or acceleration!