Functions and Patterns - Warm-up

Help and definitions

 


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Review .

EXAMPLE: We already discovered that for certain types of patterns, where the number advances by the same amount every time, that the function rule for this is jx + c where the coefficient j is the size of the step and the constant c is the amount needed to adjust the value to work for the first term. For instance:

Term n 1 2 3 4 5 6 ... n ... 200
Function f(n) 8 11 14 17 20 23 ...   ...  

The function is moving up by 3 each time so the function rule is 3n + something.

For term 1, f(1)=8, which means 3(1) + c = 8, which means c is 5.

Completing the table below looks like this:

Term n 1 2 3 4 5 6 ... n ... 200
Function f(n) 8 11 14 17 20 23 ... 3n+5 ... 605

 

For an n-sided figure, the formula for the number of total diagonals is f(n) = n(n-3)/2 .If n is the number of vertices, then n-3 is the number of diagonals out of a single vertex. The number of diagonals might seem to be n(n-3) [number of vertices times diagonals per vertex] but this ends up counting each vertex twice. Thus we divide this number by 2 and we get our formula f(n) = n(n-3)/2.