Question

The table shows the outputs y for different inputs x:

Input
(x) 5 6 7 8

Output
(y) 2 5 8 11


Part A: Do the data in this table represent a function? Justify your answer.
Part B: Compare the data in the table with the relation f(x) = 2x + 13. Which relation has a greater value when x = 7? 
Part C: Using the relation in Part B, what is the value of x if f(x) = 75?

Answer 1

A. The data represents a function because u have no repeating x values

B.
table : (5,2)(6,5)
slope = (5 - 2) / (6 - 5) = 3/1 = 3

y = mx + b
slope(m) = 3
use either of ur points (5,2)...x = 5 and y = 2
now sub and find b, the y int
2 = 3(5) + b
2 = 15 + b
2 - 15 = b
-13 = b
so the equation for this line is : y = 3x - 13

when x = 7
table : y = 3x - 13.....y = 3(7) - 13.....y = 21 - 13....y = 8
for f(x) : f(x) = 2x + 13.....f(7) = 2(7) + 13.....f(7) = 14 + 13......f(7) = 27

the relation with the greater value when x = 7 is : f(x) = 2x + 13

C. f(x) = 75
75 = 2x + 13
75 - 13 = 2x
62 = 2x
62/2 = x
31 = x <===