Part 2 | Test 4 | Time: 1 hour |
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- Solve for
*x*:

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

- Function,
- Find all the real zeros of the polynomial

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

- Determine the right-hand and left-hand behavior of the graph of
- Given
*f*(*x*)=(*x*-1)(*x*-2)(*x*+1), find*c*so that the only real zero of*f*(*x*)+*c*is -2.

**Answer:**c=12. - 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.

**Answer:**

There many other possible solutions.

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