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The graph shows the distance covered (in feet) over time (in seconds) by a turtle. We are tasked with defining the distance function for two intervals:

1. **From 0 to 2 seconds**:
   The graph starts at \((0, 0)\) and reaches \((2, 4)\), showing a straight line. This represents a linear increase in distance, so the function is:
   \[
   f(t) = 2t \quad \text{for} \quad 0 \leq t \leq 2.
   \]

2. **From 2 to 4 seconds**:
   From \((2, 4)\), the graph jumps to \((4, 12)\). This segment is also linear, and the slope can be found by:
   \[
   \text{slope} = \frac{12 - 4}{4 - 2} = 4.
   \]
   Therefore, the function in this interval is:
   \[
   f(t) = 4t - 4 \quad \text{for} \quad 2 < t \leq 4.
   \]

Would you like more details or have any questions?

Here are some related questions for further practice:
1. How do you calculate the slope of a line between two points?
2. How would the function change if the turtle stopped at 3 seconds instead of 4?
3. Can you describe the relationship between the slope and the turtle's speed?
4. What is the significance of a constant slope in a linear function?
5. How would the graph look if the turtle slowed down between 2 and 4 seconds?

**Tip**: To find the slope, use the formula \(\text{slope} = \frac{\text{change in } y}{\text{change in } x}\).

Interpret the graph and write the correspondence rules for the distance covered by the turtle in feet over time intervals.

This problem involves interpreting a linear graph of distance (in feet) versus time (in seconds) for a turtle. Learn to define piecewise functions, calculate the slope, and analyze the distance traveled over specific time intervals.

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