It is not enough to work lots of problems and get the right answer. You need to think about what you are learning, generalize ideas and form relationships from the material. These twenty questions are designed to help you accomplish this goal and hopefully to ace the final.

1. What is the standard form of a complex number? (add/subtract/multiply/divide complex numbers)
2. Name the types of equations you learned to solve in this course. Give an example of each. Solve each of your examples algebraically and graphically.
3. Illustrate the types of inequalities you learned to solve. Solve each example algebraically and graphically.
4. Give at least 3 methods of solving quadratic equations. Which method(s) can be used on any quadratic equation?
5. (a) Define what is meant by a function.
   (b) What is meant by the domain and range of a function? How can you use a graphing calculator to help you determine the domain and range of a function?
   (c) Define what is meant by a one-to one function. Illustrate this idea on a graphing calculator.
   (d) What kind of a function has an inverse function?
   (e) Complete the sentence: The graph of a function and its inverse function are reflections across __________.
   (f) How do you find the inverse of a function?
6. Define what is meant by the x- and y-intercepts of a function. What is the procedure for finding x- and y-intercepts algebraically?
7. State the formula for (a) distance between two points and (b) midpoint of a line segment.
8. Give 2 forms of the equation of a (a) parabola (b) circle.
9. Give the following forms of the equation of a non-vertical line: (a) slope-intercept form (b) point-slope form.
10. What is the slope of a horizontal line? Vertical line? Give an example of an equation of a: (a) horizontal line (b) vertical line.
11. What is the relationship between the slopes of (a) parallel lines (b) perpendicular lines?
12. (a) How can you tell from the graph of a quadratic function whether it has a maximum or a minimum value?
    (b) How would you find the maximum/minimum value of a quadratic function algebraically and graphically?
13. Give the equation of some of the basic function covered in this course and sketch the graph of each. For example: y = x, y = x², y = x³, y = |x|, y = x^(1/2), y = e^x, y = lnx.
14. For each of the functions in #13, give the equation of the function if its graph is:
    (a) translated 2 units up/down
    (b) translated 2 units left/right
    (c) reflected across the x-axis
    (d) reflected across the y-axis
    (e) reflected across the line y = x.
    Graph each basis function and your answer to (a) - (e) to verify your answers.
15. Give an example of a polynomial function. What is meant by the zeros of a polynomial function? How do you find them? Where are the zeros located on the graph of the function?
16. What is the relationship between the two functions y = b^x and y = log_bx? Graph each of these functions on a graphing calculator first using a base of 10 then using a base of e.
17. What is a logarithm?
18. Approximately what is the value of the number "e"?
19. You should be able to give the equation of the curve that might best be used to model given data. The best-fit model may be linear, quadratic, exponential or logarithmic.
20. Give one example of an application for each type of function you studied: linear, quadratic, exponential, and logarithmic.

Review from Chapter P - Course Prequisites
Old Final Exams