a) The cost of the cell phone plan at x = 0.5, x = 2, and x = 4 are:
C(0.5) = 39, C(2) = 39, C(4) = 69
b) Answers in part (a) represents the values of C at x = x₀. That is the cost of the cell phone given a certain amount of gigabytes of free data
c) C(x) is continuous at x = 2
Monthly cost of the cell phone C (x) = 39 for 0 ⩽ x ⩽ 2
Since x = 0.5 is in the range 0 ⩽ x ⩽ 2:
C(0.5) = 39
The monthly charges when given 2 gigabytes of data is $39
Since x = 2 is in the range 0 ⩽ x ⩽ 2
C(2) = 39
Since x = 4 is in the range x > 2
C(4) = 39 + 15(x - 2)
C(4) = 39 + 15 (4 - 2)
C(4) = 39 + 15(2)
C(4) = 39 + 30
C(4) = 69
b) The answers in part A represents C(x). That is, the values of C at x = x₀
c) Is C(x) continuous at x = 2
C(2) = 39
[tex]\lim_{x \to 2} C(x) = 39[/tex]
Since [tex]\lim_{x \to 2} C(x) = C(2)[/tex], the function C(x) is continuous at x = 2
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