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. (3 points)
Part B: Compare the data in the table with the relation f(x) = 2x + 13. Which relation has a greater value when x = 7? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 75?

Answer 1

A. yes...it is a function because there is no repeating x values.

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

y = mx + b

slope(m) = 3

(5,2)...x = 5 and y = 2

now we sub

2 = 3(5) + b

2 = 15 + b

2 - 15 = b

-13 = b

so the equation is : y = 3x - 13

when x = 7

y = 3(7) - 13....y = 21 - 13....y = 8

f(x) = 2x + 13...when x = 7

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

the function has a greater value

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

75 = 2x + 13

75 - 13 = 2x

62 = 2x

62/2 = x

31 = x

Explanation:

Answer 2

Part A: yes, because every input value x produces only one output value y.

Part B: in the first function, when x=7, why=8 is given
in the second function, when x=7, y=2x+13=27
so the second function has a greater value when x=7

Part C: when f(x)=2x+13=75, 2x=62, x=31