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Intermediate Algebra Extended Final Exam Review Questions

1. a) Graph the equation .
b) What is the x-intercept?
c) What is the y-intercept?
d) What is the slope of this line ?

2. a) Find the slope of the line joining the points and .
b) Find the equation of this line.

3. The equations and represent two lines that are
a) Overlapping
b) Parallel
c) Intersecting
4. Find the equation of the line through the point with .

5. Find the slope and y- intercept of the line .

6. Find the equation of the line through the point, and
a) parallel
b) perpendicular , to the line .

7. Graph the solution set of .

8. Simplify . Write all solutions using only positive
exponents.

9. Write in simplest radical form. Assume all variables are positive.

10. Write in simplest radical form. Assume all variables are positive.

11. Write in simplest form using rational exponents.



12. Simplify. Assume all variables are positive real numbers .

13. Simplify

14. Simplify:

15. Perform the indicated operation .


16. Solve each equation .

17. Use the discriminant to discuss the nature of the roots of .

18. Solve:

19. The graph of is a ___________________.
a) What is the equation of its axis of symmetry?
b) Is its vertex a maximum or a minimum point?
c) What are the coordinates of its vertex?
d) What is the y-intercept of the graph?
e) What, if any, are the x-intercepts of the graph?

20. Solve for x:



21. Define each of the following:
a) 2 linear equations are dependent
b) 2 linear equations are independent
c) 2 linear equations are inconsistent

22. Graph the system of equations , then solve it algebraically.

23. Solve each system of equations:

24. Solve the system of equations.

25. Solve the system graphically.

26. A concert sold 884 tickets. Tickets cost $5 and $8. If the total receipts were
$6,376, how many of each ticket were sold?

27. Find the domain and range of the relation:
. Also find the domain and range of the inverse of
this relation.

28. If , find
and
.
29. Find the inverse of the function .

30. a) Write in exponential form.
b) Write in logarithmic form .
31. Write as a sum or difference of logarithms :

32. Write as a single logarithm with a coefficient of 1.

33. Find:

34. If , find x.

35. Graph each of the following functions:


36. Solve for x:


37. Find x if .

38. Solve for x.

SOLUTIONS

19. The graph is a parabola .

21. a) The lines coincide. There are infinitely many solutions.
b) The lines intersect at one point.
c) The lines are parallel. There is no solution.

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