Question

Use the given table to determine the appropriate model of the function. x       1             2             3             4             5       f(x)       18             14             10             6             2       linear exponential cubic quadratic

Answer 1

It is linear

Explanation:

Due to the pattern in the table the common difference it always 4. For example, 18-14=4 . 14-10=4 and so on.

Answer 2

Here the difference between two consecutive x terms =14-18=-4

And we have to use the following formula

f(x) = a + (x-1)d

Substituting the values of first term, a common deifference,d, we will get

f(x) = 18+(x-1)(-4)

f(x) = 18 -4x+4

f(x) = 22-4x

So the required model for the given table is f(x) = 22-4x .