Precalculus Practice Exam

Part 2 Test 4 Time: 1 hour

1. Solve for x:

Answer: The solution set consists of all x satisfying , or in interval notation, .

2. Define and give a graphical example of the following terms:

• Function,

Answer: A function is a rule which associates to each element in the domain exactly on element in the range.

• One-to-one function,

Answer: A function is one-to-one if two different values in the domain are mapped to two different values in the range.

• Polynomial function, and

Answer: A polynomial function is a function of the form

• Rational function.

Answer: A rational function is the quotient of two polynomials.

3. Find all the real zeros of the polynomial

Answer: The real zeros are x=2, x=1, and .

4. Given the function where a,b,c,d,e and f are integers and a>0,

• Determine the right-hand and left-hand behavior of the graph of f(x).

Answer: The graph of f(x) approaches on the left and on the right.

• If -5 and 5 are zeros of f(x), and if f(-2)=12, f(0)=-18,and f(2)=50, how many real zeros does the function f(x) have?

Answer: The function has at least four distinct real zeros. If counted according to multiplicity, the function has five real roots (x=5 might be a double root).

5. Given f(x)=(x-1)(x-2)(x+1), find c so that the only real zero of f(x)+c is -2.

6. Find a polynomial of degree 10 that has zeros 2-3i,7,8,-4, and 5-i. You do not have to simplify your answer.

There many other possible solutions.

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Mon Jun 30 12:52:11 MDT 1997