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
