Question

Which of the following function notation describes the ordered number pair P(x) = {(1,6), (2,11), (3,16), (4,21)}?

Answer 1

your question is incomplete , complete question is ------> Which of the following function notation describes the ordered number pair P(x) = {(1,6), (2,11), (3,16), (4,21)}?

Select one:
a. f(x) = 5x + 1
b. f(x) = 5x - 1
c. f(x) = x + 6
d. f(x) = 11/5x


answer :- option (a)

explanation :- here you see all options are linear variable except (d) . [ well, you can see (d) 11/5x doesn't possible because at x = 1 , P(1) ≠ 6 , it is 11/5 ]

now, Let P(x) = ax + b
put x = 1 and P(1) = 6
6 = a + b ......(1)

put x = 2, P(2) = 11
11 = 2a + b ......(2)

solve equations (1) and (2),
a = 5 and b = 1

so, P(x) = 5x + 1
now you can check rest ordered numbers.
at x = 3 , P(3) = 5× 3 + 1 = 16 ✓
at x = 4 , p(4) = 5 × 4 + 1 = 21 ✓
hence,it is clear that P(x) = 5x + 1