Determine the function rule Input 4 7 Output 11 13SolutionTh

Determine the function rule:

Input: 4 7

Output: 11 13

Solution

The input-output table is as under:

Since there are only 2 input-output sets are given, the best way to find the function rule is to determine the equation of the line which passes through these points. We know that the equation of the line which passes through the points ( p, q) and ( r, s) is y-q = m( x-p), where m is the slope. Also, m = (s - q) / (r -p). Thus, the equation of the line, which passes through the points ( 4,11) and (7, 13) is y - 11 = m (x - 4). Also m = (13 -11) / (7 - 4) = 2/3. Then the required function rule is y - 11 = 2/3 (x -4) or, y = (2x/3) + 11 - 8/3 or, y =( 2x/3) + 25/3 or, y = 1/3 ( 2x+ 25)