Question

Below is the table of values of a function. Write the output when the input is

input 4 , 7 , 9 , n
output 1 , 4 , 6 __ blank

Answer 1

equation

Answer 2

The given table of values for the function is:

input: 4, 7, 9, n
output: 1, 4, 6, __

Based on the given values, we can observe that the output increases by 3 units each time the input increases by 3 units. Hence, we can determine the next output for the input "n" by adding 3 to the previous output:

When the input is "n", the output would be 6 + 3 = 9.

Therefore, the missing number in the output sequence is 9.

Answer 3

Based on the given table of values, we can try to find an equation that relates the input and output values.

Let's analyze the data:
- When the input increases by 1 (from 4 to 7), the output increases by 3 (from 1 to 4).
- When the input increases by 2 (from 7 to 9), the output increases by 2 (from 4 to 6).

From this pattern, we can observe that the rate at which the output increases is decreasing. This suggests that the relationship between the input and output is not linear.

One possible equation that fits the given data is a quadratic equation. Let's try to fit a quadratic equation of the form y = ax^2 + bx + c to the data points:

Given data:
input: 4, 7, 9
output: 1, 4, 6

Let's substitute the input and output values into the equation:
1 = a(4)^2 + b(4) + c
4 = a(7)^2 + b(7) + c
6 = a(9)^2 + b(9) + c

Now, we have a system of three equations with three unknowns (a, b, and c). We can solve this system of equations to find the values of a, b, and c, which will give us the desired quadratic equation that relates the input and output.

Solving the system of equations will give us the specific equation that fits the given data points.