The table shows the outputs, y, for different inputs, x:
Input (x) 6 12 15 25
Output (y) 14 15 15 16
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) = 7x − 15. Which relation has a greater value when x = 6? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 6? (5 points)
(10 points)
Part A: To determine if the data in the table represents a function, we need to check if each input value has a unique output value. In this case, the input values are 6, 12, 15, and 25, and the corresponding output values are 14, 15, 15, and 16. We can see that the input value of 15 has two different output values, which means that the data in this table does not represent a function since a function can have only one output for each input.
Part B: To compare the data in the table with the relation f(x) = 7x - 15, we need to substitute x = 6 into both the table and the relation and compare the output values.
Using the table: When x = 6, the output (y) is 14.
Using the relation: f(6) = 7(6) - 15 = 42 - 15 = 27.
Comparing the two, we can see that the relation f(x) = 7x - 15 has a greater value when x = 6, with an output of 27 compared to the output of 14 in the table.
Part C: To find the value of x when f(x) = 6 using the relation f(x) = 7x - 15, we can set the equation equal to 6 and solve for x:
7x - 15 = 6
7x = 6 + 15
7x = 21
x = 21/7
x = 3
Therefore, the value of x when f(x) = 6 using the relation is x = 3.