Question

How do you explain this function?

Answer 1

Hello from MrBillDoesMath!

Answer:

For  0 <= x < =40 the function is that of the straight line 15x which has slope 15. Note that at x = 40 the value of the function is 15(4) =600

For x > 40 , the function is another straight line but with slope 20. This line is steeper than the 15x line but for x near, but slightly greater than  40, the value is close to 600 + 20 (40-40)  or 600 + 20(40-40) = 600.  This is the same value as the first line, 15x, at x = 40.

In summary, the graph of p(x), from   0 <= x <=40, is a line of slope 15 and for x>40 is a line of slope 20.  p(x) has a removable discontinuity at x = 40 because  p(x) approaches 600 as x approaches 40, regardless of the method of approach (i.e. whether x  approaches 40 from values less than 40 or from values greater than 40)

Thank you,

MrB