Pre-Calculus Problems

1. Analyze the graph of the function

F(x)= x2+x-56/x+7

a) What is the domain of F(x)?
b) What is the equation of the vertical asymptote(s) of F(x)?

2. Solve the inequality algebraically.

10x-8 ? 3×2

3. Answer the questions about the following inequality

30x-11>30/x

a) Is the point x=0 included in the solution set of the inequality?
b) Are the other finite end points of the interval included in the solution set?
c) What is the solution set?

4. Use the remainder theorem to find the remainder when f(x) is divided by x- 1/5. Then use the factor theorem to determine whether x- 1/5 is a factor of f(x).

f(x)=5×4-x3+5x-1

5. Use the rational zeros theroem to list the potential ratonal zeros of the polynomial function. Do not attempt to find the zeros.

f(x)=33×4+28×3+66×2+196x+63

6. Solve the equation in the real number system.

7×4-106×3+351×2-356x+44=0

7. Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.

Degree 6; zeros: -5, 3+i, -8-i,2

8. Form a polynomial f(x) with real coefficients having the given degree and zeros.

Degree 4; zeros: 5-4i;5 multiplicity 2

9. Find the complex zeros of the polynomial function. Write f in factored form.

f(x)=3×4-10×3+15×2+20x-8