The table shows the outputs y for different inputs x:
Input
(x) 3 7 11 15
Output
(y) 4 6 8 10
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) = 5x – 21. Which relation has a greater value when x = 11? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 99? (5 points)
A) sure there is one value of y for every value of x
B) in table y = 8
in function
y = 5(11) - 21 = 55-21 = 34
C) 99 = 5 x - 21
5 x = 120
x = 24
well i do not the answer
Part A: Yes, the data in this table represent a function. A function is a relation where each input (x) is associated with only one output (y). In this table, each input (x) has a unique output (y), so it satisfies the definition of a function.
Part B: To compare the data in the table with the relation f(x) = 5x – 21, we substitute x = 11 into both the table and the relation:
For the data in the table:
x = 11
y = 8
For the relation f(x) = 5x – 21:
f(11) = 5(11) – 21
f(11) = 55 – 21
f(11) = 34
Comparing the two, the relation f(x) = 5x – 21 has a greater value of 34 when x = 11.
Part C: Using the relation in Part B, we need to find the value of x if f(x) = 99:
f(x) = 99
5x – 21 = 99
5x = 99 + 21
5x = 120
x = 120/5
x = 24
Therefore, the value of x if f(x) = 99 is 24.
Part A: To determine if the table represents a function, we need to check if there is exactly one output (y) for each input (x) value. In this table, each input has a unique output. For example, x = 3 corresponds to y = 4, and x = 7 corresponds to y = 6. Since there is no repetition of input-output pairs, the data in this table represents a function.
Part B: The given relation is f(x) = 5x - 21. To compare this relation with the data in the table, we can substitute the value x = 11 into both the relation and the table.
Using the relation:
f(11) = 5(11) - 21
f(11) = 55 - 21
f(11) = 34
Using the table:
The output (y) for x = 11 is 8.
Comparing the values, we can see that the relation f(x) = 5x - 21 has a greater value (34) when x = 11 than the table (8).
Part C: To find the value of x when f(x) = 99, we can set up the equation:
99 = 5x - 21
To solve for x, we need to isolate it on one side of the equation. Adding 21 to both sides:
99 + 21 = 5x - 21 + 21
120 = 5x
Now, divide both sides by 5:
120/5 = 5x/5
24 = x
So, when f(x) = 99, the value of x is 24.