State the end behavior for the following polynomials. Use symbolic notation.

1.  f(9x) = (x - 5)

 

2.  f (x) = - 12x + 9

Create a possible polynomial function from the given roots, and then state the maximum number of turning points and state the end behavior.

1. {-3,5}

2. {-2, 1, 4}

3. {-2, 0 multiplicity of 2, 1}

4. {2 multiplicity of 2, 3 multiplicity of 2}

Consider the following polynomials in ℙ₃:

q(x) = 2x³+3x²âˆ’2x+1
r(x) = 6x³+8x²âˆ’x+2
u(x) = x³âˆ’x²+7x−2

For each of the following polynomials, determine whether it is in span{q, r, u}. If so, express it as a linear combination of the polynomials above.
Use, e.g., q rather than q(x) to represent the polynomials in your linear combination.

p1(x) = 4x³+6x²âˆ’4x+2 [select answer]
p2(x) = -5x³+x²âˆ’8x-8 [select answer]
p3(x) = -9x³âˆ’14x²+7x−5 [select answer]