Which function rule represents the data in the table below?
Input (x)
1
2
3
4
5
Output (y)
9
14
19
24
29
A. y = 4 + 5x
B. y = 3 + 6x
C. y = 5 + 4x
D. y = 6 + 3x
C. y = 5 + 4x
To determine the function rule that represents the given data, we can look for a pattern between the input (x) and output (y) values.
By observing the data, we can see that the output (y) increases by 5 each time the input (x) increases by 1. This means that the coefficient for x in the function rule will be 5.
Now let's find the constant term in the function rule. We can take any x and y value from the table and substitute it into the function rule to find the constant term. For example, using the first data point (x = 1, y = 9):
9 = 5 + 4(1)
Simplifying the equation, we have:
9 = 5 + 4
9 = 9
Since the equation is true, the constant term is 5.
Combining the coefficient for x and the constant term, we have the function rule:
y = 5 + 4x
Therefore, the correct answer is C. y = 5 + 4x.