The function P, whose graph follows, gives the prime rate (the interest rate banks charge their best corporate customers) as a function of time for the first 32 wk during a year. Determine the values of t for which P is discontinuous.
A) t = 11
B) t = 3, 2, 5
C) t = 8, 2, 5
D) t = 8, 16, 20

Question

The function P, whose graph follows, gives the prime rate (the interest rate banks charge their best corporate customers) as a function of time for the first 32 wk during a year. Determine the values of t for which P is discontinuous. ​  ​
A) t = 11 
B) t = 3, 2, 5 
C) t = 8, 2, 5 
D) t = 8, 16, 20

Quizplus · Accepted Answer

The graph has a jump discontinuity at t = 8, meaning that there is a sudden increase in the prime rate at that point. There are also two vertical asymptotes at t = 16 and t = 20, indicating that the prime rate becomes unbounded (either very large or very small) as time approaches those values. Therefore, the correct answer is D, with t = 8, 16, and 20. There are no other points of discontinuity on the graph.

The Function P, Whose Graph Follows, Gives the Prime Rate