End Behavior and Domain and Range of Polynomials
Where is this function going as x goes to the left?
f(x) = -3x4
- infinity
y = 10
yes
Find the zeros.
y = x2 - 4
-2, 2
Add.
(2x2 + 3x + 2) + (3x2 - 5x - 1)
5x2 - 2x + 1
Multiply.
3x6(4x2)
12x8
Where is this function going as x goes to the right?
f(x) = 3x + 1
infinity
y = 2x2 + 1/2
yes
Find the zeros. Round to three decimal places.
y = 3x3 - 16
~1.747
(2x3 + 4x2 - 3x + 1)+(5x2 + 2x - 1)
2x3 + 9x2 - x
Multiply.
(9x + 4)(2x - 1)
18x2 - x - 4
What is the domain of f(x) = 4x3 + 2?
All real numbers
y = 3x-2 +4x-1
no
Find the zeros. Round to three decimal places.
y = 4x4 - 16
~-1.414, 1.414
Subtract.
(3x + 2) - (4x - 2)
-x + 4
Divide.
(x3 + 3x2 - 28x - 62)/(x + 6)
x2 - 3x - 10 - 2/(x+6)
What is the range of f(x) = 3x2?
y >= 0
y = 1/x + 3
no
Find the zeros.
y = 3x2
0
Subtract.
(3x2 - 5x + 5) - (6x + 2)
3x2 - 11x + 3
Divide.
(a3 - 4a2 +5a - 55)/(a - 5)
a2 + a + 10 - 5/(a - 5)
Write the end behavior for this function?
f(x) = 3x3 - 2
As x to - infinity, y to - infinity.
As x to infinity, y to infinity.
Name three examples of expressions that are NOT polynomials.
answers vary
Name two other names for zeros of a polynomial.
Roots, x-intercepts
Add.
(4x + 4 - 12x2 - 11x4) + (3x2 - 5x -10 + 6x3)
-11x4 + 6x3 - 9x2 - x - 6
What is the remainder?
(-4x2 - 24 + x4 - 9x)/(x + 2)
-6