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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 xaxis:
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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