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 ay-intercept of 0 (continue the line back to they-axis). If you didn't get the same slope values, it's likely because you didn't notice the different scales on thex-axis andy-axis. They-axis is going up by 1, whereas thex-axis is going up by 0.5. Final answer should look like this: