Study Notes on Function Analysis and Range Calculation

Data Table Analysis

  • Data values for variables y and x are presented.
  • Several pairs from the data are listed as:
    • (x, y) pairs:
      • (-3, -0.6)
      • (1, 0.2)
      • (7, 1.4)
      • (-5, -10)
      • (-2, -1)
      • (4, 17)
      • (50, -58)
      • (-2, 8)
      • (2, -18)

Function Definition and Range Calculation

  • A function is defined as:

    • f(x)=4x+5f(x) = 4x + 5

  • Given that the domain of the function is specified as:

    • 0≤x≤500 \leq x \leq 50

  • Finding the Range:

    • The range of a function is the set of values that the function can take, depending on its domain.
    • Calculate the minimum value of f(x):
      • When x=0x = 0:
      • f(0)=4(0)+5=5f(0) = 4(0) + 5 = 5
    • Calculate the maximum value of f(x):
      • When x=50x = 50:
      • f(50)=4(50)+5=200+5=205f(50) = 4(50) + 5 = 200 + 5 = 205

  • Thus, the range for the given domain is:

    • 5≤f(x)≤2055 \leq f(x) \leq 205

Conclusion

  • The final conclusion drawn from the calculations is that the range of the function f(x)=4x+5f(x) = 4x + 5 for the domain specified is:
    • Range: [5,205][5, 205]