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Classify by Highest Degree
Classify by Number of Terms
End Behavior
What is the maximum number of curves?
Synthetic Substitution Setup
100
f(x) =6
Constant
100
f(x) =14
Monomial
100
y = 3x - 9
Left side faces up. Right side faces down.
100
y = - 3x - 9
0 (straight line)
100
How do I determine what number goes in the box on the left?
The number that I'm plugging in f(x)
200
f(x) = -2x^2+4x-9+3x^3
Cubic
200
F(x) = 2x+19
Binomial
200
f(x) = -3x^2 +14
As x approaches -infinity, y approaches -infinity. As x approaches +infinity, y approaches -infinity. Or Both sides face down
200
f(x) = 3x^2 +14
1 (Parabola)
200
How do I figure out what goes in the second row of a Synthetic Substitution Problem?
By multiplying the sum of the previous column with the f(x) from the box on the left.
300
f(x) = 2x^4-9
Quartic
300
f(x) = 3x^3-2x^2+4x-9
Polynomial
300
f(x) = x^3 - 2x^3 -5
As x approaches -infinity, y approaches -infinity. As x approaches +infinity, y approaches infinity. Right sides opens up; left side opens down
300
f(x) = 3x^3-2x^2+4x-9
2 (Cubic)
300
How do I figure out what numbers go in the first row of a Synthetic Substitution problem?
By using the coefficients of the original problem (and using 0 for any terms that aren't there)
400
f(x) = -3x^2 -5 + 4x^3
Cubic
400
f(x) = -3x^2 -5 + 4x^3
Trinomial
400
f(x) = -3x^2 - 14x +6
As x approaches -infinity, y approaches - infinity. As x approaches +infinity, y approaches - infinity. Or Both sides face down
400
f(x) = 5x^3 + 3x^4 - 2x^2 -3x +4
3 (Quartic)
400
Where does the answer show up in a Synthetic Substitution problem?
In the third row under the Constants column.
500
f(x) = 7x - 4x^2 -14
Quadratic
500
f(x) = 7x - 4x^2 -14 + 2x^2
Trinomial
500
f(x) = 4x^4 - 3x^2 - 2x +3
As x approaches -infinity, y approaches infinity. As x approaches +infinity, y approaches infinity. Or Both sides face up
500
f(x) = 7x^7 - 4x^4 + 2x^2 -3
6 (septic)
500
How do you get the numbers in the bottom line of a Synthetic Substitution problem? (2 Answers)
The First Number is determined by the Leading coefficient. All the other numbers can be bound by adding up the totals in Row 1 and Row 2.