Create a table of values for f(x) = 40 if x ≤ 2 and 40+8(x-4) if 4 ≤ x ≤ 8 and graph it (piecewise function)

Here is the table of values for the given piecewise function \( f(x) \):

| \( x \) | \( f(x) \) |
|--------|------------|
| 0      | 40         |
| 1      | 40         |
| 2      | 40         |
| 4      | 40         |
| 5      | 48         |
| 6      | 56         |
| 7      | 64         |
| 8      | 72         |

The graph of the function is shown as well, with the piecewise behavior clearly visible.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. What happens to the function \( f(x) \) when \( x = 3 \)?
2. How does the slope of the function change for \( x > 4 \)?
3. Can this piecewise function be extended for \( x > 8 \)?
4. How would the function look if the second part were \( 40 + 5(x-4) \) instead of \( 40 + 8(x-4) \)?
5. What is the derivative of the second part of the piecewise function?

**Tip:** For piecewise functions, always check for continuity and differentiability at the breakpoints (in this case, at \( x = 2 \) and \( x = 4 \)).

Learn how to create a table of values and graph a piecewise function with two parts: f(x) = 40 for x ≤ 2 and f(x) = 40 + 8(x - 4) for 4 ≤ x ≤ 8. Explore key concepts such as continuity at breakpoints and the slope of a linear function. Suitable for students in Grades 9-11.

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