I wanted to ask when the function for #12 would remain continuous, since I though it would be continuous from 0<p<15 and p>15, although the textbook corrections had a slightly different answer.
Also, for #15, how would you find the expression? Because I found the slope and y-intercept for the notation, but I did not get the right answer.
Your answer for the first question (#12) is correct. You should also state that it's discontinuous at p=15, since the question asks for where it's discontinuous too.
For the second question (#15), the line on the left has a slope of 3 and a y-intercept of -1. The line on the right has a slope of -1 and a y-intercept of 0 (continue the line back to the y-axis). If you didn't get the same slope values, it's likely because you didn't notice the different scales on the x-axis and y-axis. The y-axis is going up by 1, whereas the x-axis is going up by 0.5. Final answer should look like this: