Question 198174
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You say:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(x) = -4x - 8].

That means if we substitute any pair of values from your table for *[tex \LARGE x] and *[tex \Large f(x)], then we should have a true statement.  Let's try it:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -8 =^? -4(2) - 8 = -8 -8 = -16].

Oops!  First one fails. So we can guarantee that your function is not the one we are looking for.  Back to the drawing board -- literally.

First thing to do is to create four ordered pairs from the pairs of numbers in your table.  (2, -8), (3, -12), and so on.  Then plot these points on a graph (see I told you we were going back to the drawing board).  If you plot them correctly, you will see that they all lie in one straight line.

Since the points all lie in a straight line, we know that we have a linear function.  All you need to do now is pick two of the pairs and use the two-point form of the equation of a line to develop your function:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(x) - y_1 = \left(\frac{y_1 - y_2}{x_1 - x_2}\right)(x - x_1) ]

Substitute the coordinates from any two of the points and then do the arithmetic and solve for *[tex \Large f(x)]

John
*[tex \LARGE e^{i\pi} + 1 = 0]
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