Find the function rule.

1.  x| -3| -2| -1| 0| 1| 2|  3
 f(x)| 10|  5|  2| 1| 2| 5| 10

Let's compare f(x) to x²

1.  x| -3| -2| -1| 0| 1| 2|  3
   x²|  9|  4|  1| 0} 1| 4|  9
 f(x)| 10|  5|  2| 1| 2| 5| 10

Each value of f(x) is 1 more than the square of x,

So f(x) = x²+1


2. x| -6| -4| -2| 0| 2|  4|  6
f(x)| 71| 31|  7|-1| 7| 31| 71

Let's also compare this one to x²

2. x| -6| -4| -2| 0| 2|  4|  6
  x²| 36| 16|  4| 0} 4| 16| 36
f(x)| 71| 31|  7|-1| 7| 31| 71

That compares to 2x²

2. x| -6| -4| -2| 0| 2|  4|  6
  x²| 36| 16|  4| 0} 4| 16| 36
 2x²| 72| 32|  8| 0} 8| 32| 72
f(x)| 71| 31|  7|-1| 7| 31| 71

Each value of f(x) is 1 less than twice the square of x,


So f(x) = 2x²-1

Edwin