Math Problem Statement
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)
Solution
Here is the table of values for the given piecewise function :
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:
- What happens to the function when ?
- How does the slope of the function change for ?
- Can this piecewise function be extended for ?
- How would the function look if the second part were instead of ?
- 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 and ).
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Linear Functions
Function Graphing
Formulas
f(x) = 40 if x ≤ 2
f(x) = 40 + 8(x - 4) if 4 ≤ x ≤ 8
Theorems
Continuity at breakpoints
Slope of a linear function
Suitable Grade Level
Grades 9-11