Final answer:
The values of the given functions at the specified inputs are: H(-6) = 48, P(7) = 42, F(2) = -16, and P(-8) = -12. These results are obtained by substituting the respective inputs into the corresponding functions: H(n) = 3|3x+2|, P(x) = 3|-2x|, F(x) = -2|3x+2|, and P(a) = a - 4.
Step-by-step explanation:
There are four functions to evaluate: H(n), P(x), F(x), and P(a). We need to find the value of each function at the given input. To find H(-6), substitute -6 for n in H(n) = 3|3x+2| to get H(-6) = 3|3(-6)+2| = 3|-18+2| = 3|-16| = 3(16) = 48. To find P(7), substitute 7 for x in P(x) = 3|-2x| to get P(7) = 3|-2(7)| = 3|-14| = 3(14) = 42. To find F(2), substitute 2 for x in F(x) = -2|3x+2| to get F(2) = -2|3(2)+2| = -2|6+2| = -2|8| = -2(8) = -16. For the function P(a) = a - 4, we find P(-8) by substituting -8 for a to get P(-8) = -8 - 4 = -12.