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 f(x)f(x):

xxf(x)f(x)
040
140
240
440
548
656
764
872

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)f(x) when x=3x = 3?
  2. How does the slope of the function change for x>4x > 4?
  3. Can this piecewise function be extended for x>8x > 8?
  4. How would the function look if the second part were 40+5(x4)40 + 5(x-4) instead of 40+8(x4)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=2x = 2 and x=4x = 4).

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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