1. The equation of the x-axis is __________ and the
equation of the y-axis is __________

2. The equation of the unit circle is ______________

3. For the polynomial -2x^{4} + 5x^{2} − 2x -5 the degree is _____, the leading
coefficient is _____ and the constant is _____

4. A polynomial with degree 5 has at most ______ zeros.

5. If
is a root of a polynomial with integer coefficients, then so is __________

6. The expression | x − 5 | ≥ 7 means the distance between ____ and ____ is
greater than or equal to_____. Therefore the solution will contain _____
interval(s).

7. An even function is symmetric with respect to __________, whereas an odd
function is symmetric with respect to _______________.

8. An example of an even function is ___________________, and an example of an
odd function is ____________________.

9. A function is one to one if ________________________________________________

10. Any line defines a function except a ____________________ line.

11. The slope of a horizontal line is ______________, whereas the slope of a
vertical line is _______________.

12. The graph of y = x^{2} looks like

13. The graph of y = (x - 1)^{2} + 2 looks like

Problems 14 through 23 are worth 4 points each.

14. Find the distance between the points (2,5) and (-4,3), and find the
midpoint.

Distance ____________ Midpoint ( , )

15. Simplify the compound fraction:

16. Factor the difference of two cubes: x^{3} − 8y^{3}

17. Rationalize the denominator:

18. Simplify, using positive exponents only:

19. Write the equation for the circle with center (0,0) and radius 2.

20. Find the domain of the function

21. Solve the equation (x + 5)^{2} = 9

22. Solve the equation x^{2} −2x − 6=0

23. Solve the inequality |x − 5| ≥ 2. Write your answer in interval notation.

Problems 24 through 34 are worth 5 points each.

24. Find the inverse of the function f(x) = 2x − 3.

25. Find the equation of the line through the points (1,3) and (6,-2). Write
your answer in the slope intercept form, i.e. in the form y = mx + b

26. Write the equation for the line with slope 2 through the point (1,5)

For 27 and 28, let

27. Find

28. Find f ◦ g and g ◦ f

29. Find the vertex and intercepts for the graph of y = x^{2} - 2x - 3

30. Use synthetic division to show that –1 is a root of f(x)= 2x^{3} + 3x^{2} - 5x -
6, and factor f(x) into a linear factor times a quadratic.

31. Find the other two roots for the function in problem 30.

32. Write the function in factored completely as a product of three linear
factors.

33. Find the horizontal and vertical asymptotes if any for the functions

34. Write the partial fraction decomposition for the rational expression