Question 295569: When dealing with Functional Relationships I need to know what the equation to represent each function is with the table provided. The table is an input/output table. The input numbers are: 5, 6, 7, 8, and 9. The output numbers are: 5, ?, 9, 11, and 13. I know that the ? is 7, just by the pattern. What I don't know is what equation could I write to give me that in every instance?
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! Let's look at the input output
5 5 diff 0
6 ? diff ?
7 9 diff 2
8 11 diff 3
9 13 diff 4
y=5+(x-5)*2
let's try it
y=5+(5-5)*2=5+0=5
y=5+(6-5)*2=5+2=7
y=5+(7-5)*2=5+4=9
y=5*(8-5)*2=5+6=11
y=5+(9-5)*2=5+8=13
Works every time.
We could also have
y=x+(x-5)
y=5+0
y=6+1
y=7+2
y=8+3
y=9+4
Why do they both work?
reduce the first
y=5+(x-5)*2
y=5+2x-10
y=2x-5
reduce the second
y=x+(x-5)
y=2x-5
because they both are equal to y=2x-5
So the best equation is y=2x-5
which saves on calculations
y=10-5=5
y=12-5=7
y=14-5=9
y=16-5=11
y=18-5=13
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