Hi please help me I got stuck!

  output = n - 3

Step-by-step explanation:

When you're trying to determine the functional relationship between values in a given set of points, there are a few things you can look at.

If the relation is a proportion, the ratio of output to input values will be a constant. Here, those ratios are 1/4, 3/6, 6/9 = 1/4, 1/2, 2/3. These values are different, so we know we're not dealing with a proportion.

If the input values are evenly spaced, you can look at first differences. Here, they're not, so we look at the ratios of first differences:

  (y2 -y1)(x2 -x1) = (3-1)/(6-4) = 2/2 = 1

  (y3 -y2)/(x3 -x2) = (6-3)/(9-6) = 3/3 = 1

These ratios are the same (1), so you know the relation is linear, and it has a slope of 1. This is enough information to make use of the point-slope form of the equation for a line. Using the first input-output pair, we have ...

  y -1 = 1(x -4)

  y = x -4 +1

  y = x -3

We are told to use 'n' as the input value, so we can write this as ...

  output = n - 3

Additional comment

We came to a conclusion before we got to the last thing we could look at. The number of points given (here, 3) will be one greater than the degree of the polynomial the table can represent. Here, we're given 3 points, so the highest-degree function that the table could represent is 2nd degree, a quadratic.

3 points (not on a line) can always be matched by a quadratic function. They might also be matched by an exponential function, so one of the things you can check is to see if the output values are some number raised to the power of the input.

x^6

step-by-step explanation:

this is correct because:

x-6=0

0*x=0

so

x^6

step-by-step explanation: