This question is about family functions.
If we want to know which family this sequence represents we must see if there's a pattern among the values for x and the values for f(x).
First I see that on the left column of the table x increases by 1 every time:
-1 , if I add +1 , we get
0 , if I add +1, we get
1 and so on
2
3
Now I can also see on the right column that f(x) increases by 2 every time.
-3 , if I add +2, we get
-1 , if I add +2, we get
0 , and this goes on and on
3
5
What have we found out? As x increases by 1 , f(x) increases by 2 as well.
A function that has this behavior must be a linear function.
A linear function has the following form: y = f(x) = a + bx
And that's how we know if the sequence is linear.
So, the idea is always see the how x behaves from one roll to the other as well as how f(x) behaves.
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A function is linear if both x and f(x) are increasing or decreasing constant:
* If x increases, f(x) must increase as well
* If x decreases, f(x) must decrease too
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