# Polynomials and Rational Functions

Find the vertex of the parabola :

1. x^{2} + 3x + 3

Graph by hand by finding the vertex, axis of symmetry, x and y intercepts,
leading

coefficient , and extra points. Give the domain and range of the function:

2. x^{2} – 7x + 12

Find the zeros of the function , state the multiplicity, and state if the line
crosses or touchs

the x-axis:

3. 2x^{3} – 4x^{2} + 2x

Prove the function has a zero within the interval by using the Intermediate
Value

Theorem:

4. f(x) = x^{4} – x^{3} + 3x^{2} – 5; (0, 2)

Divide using long division:

5. (6x^{2} + 3x^{4} – 3x + 2) ÷ (x + 3)

Divide using synthetic division :

6. (7x – 5x^{5} + 4x^{2} –8) ÷ (x + 3)

List all possible zeros and find all zeros of the function.

7. x^{3} – x^{2} – x – 2 = 0

Find all zeros of the function by using the Rational Zero Theorem, Descartes'
Rule of

Signs and quadratic formula .

8. 4y^{5} + 12y^{4} – 41y^{3} – 99y^{2} + 10y + 24 = 0

Graph the function by finding horizontal, vertical, and/or slant asymptotes,
symmetry, x

and y intercepts , and extra points if possible.

Solve the inequality and write answer in interval notation.

Solve :

14. The cost of a product is a function of the number of products produced as
given in the

equation where x is the number of products produced and C(x) is in dollars.

a. Find and interpret C(20), C(40), and C(60).

b. Where is the vertical asymptote?

c. Graph the function .

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