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

the data in the table does represent a function because there is no repeating x values.

f(x) = 2x + 13.....f(7) = 2(7) + 13....f(7) = 14 + 13 ...f(7) = 27

the table :

(5,2)(6,5)

slope = (5-2) / (6-5) = 3

y = mx + b

2 = 3(5) + b

2 = 15 + b

2 - 15 = b

-13 = b

equation : y = 3x - 13...when x = 7

y = 3(7) - 13

y = 21 - 13

y = 8

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

f(x) = 2x + 13...when f(x) = 75

75 = 2x + 13

75 - 13 = 2x

62 = 2x

62/2 = x

31 = x

Explanation:

Answer 2

the data in the table does represent a function because there is no repeating x values.

f(x) = 2x + 13.....f(7) = 2(7) + 13....f(7) = 14 + 13 ...f(7) = 27

the table :
(5,2)(6,5)
slope = (5-2) / (6-5) = 3
y = mx + b
2 = 3(5) + b
2 = 15 + b
2 - 15 = b
-13 = b
equation : y = 3x - 13...when x = 7
y = 3(7) - 13
y = 21 - 13
y = 8

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

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