## Math 116 Study Guide - Final Exam

1. You are given a function, a domain and range. You need to indicate the translation and the new domain and range. Six parts.
2. Identify the conic section or degenerate case. No answer is duplicated. Nine parts.
3. Find the inverse of a function. Concentrate on problems with restricted domains.
4. Solve a 2x2 system of linear equations by graphing.
5. Solve a 2x2 system of linear equations by substitution.
6. Solve a 2x2 system of linear equations by addition/elimination.
7. Solve a 2x2 system of linear equations by Cramer's Rule.
8. Solve a 2x2 system of linear equations by Gauss-Jordan elimination.
9. Solve a 2x2 system of linear equations by Matrix Algebra (inverses of matrices).
10. Evaluate the difference quotient for the given function. You need to know what the difference quotient is.
11. Write a function which has the indicated zeros.
12. Linear programming problem. You need to sketch the region, identify the corner points, and then find the maximum or minimum value of the objective function.
13. Setup, but do not solve, a system of linear equations which can be used to find the equation of the parabola passing through three points.
14. Multiply two matrices.
15. Find the inverse of a 2x2 matrix.
16. Find the determinant of a 2x2 matrix.
17. Given a polynomial function ...
1. List all possible combinations of the number of total, positive, negative, and complex solutions.
2. List all possible rational roots of the function.
3. Find all the real and complex zeros of the function.
4. Completely factor the function using linear and irreducible quadratic factors.
18. Sketch a rational function
19. Find the partial fraction decomposition.
20. Sketch the graph of a conic section. The conic section is already in standard form.
21. Solve a logarithmic equation for x.
22. Solve a matrix equation for X.
23. Identify the term, rule, or theorem defined or which is applicable. You should know the following: Fundamental Theorem of Arithmetic, Fundamental Theorem of Algebra, Fundamental Theorem of Linear Programming, Fundamental Counting Principle, Descartes' Rule of Signs, Rational Root Theorem.; Definitions of circle, ellipse, parabola, hyperbola, combination, permutation. Eight parts.
24. Identify each statement as true or false. You should concentrate on the following
1. Elementary row operations.
2. Matrix multiplication.
3. Melodic properties of logs.
4. Determinants of special matrices.
5. Relationship of a matrix inverse to its determinant.
6. Relationship of a matrix inverse to its size.
7. Limit definition of e.
8. One-to-one functions in regards to line tests.
9. Matrix division.

### Notes

Points per problem
 1 2 3 4 5 6 7 8 9 10 11 12 12 9 6 6 6 6 6 6 6 6 6 10 13 14 15 16 17 18 19 20 21 22 23 24 6 6 6 6 20 10 6 6 6 6 16 18

• The final is open notebook.
• You may have the study guides in the notebook.
• Your book does not count as your notebook. If you took notes in your book and you want to use them on the final, then transfer them to paper, and stick them in your notebook.
• Go through and answer as much as you can first without going to your notebook. When you go to your notebook, your productivity greatly decreases.
• You will not have enough time to take the exam if you have an unorganized notebook and have to search through it to find the information. Go through ahead of the test and organize your notebook.
• A good idea is to take the study guide and write where that information is in your notes.
• The exam is Wednesday, December 18, from 10:00 to 11:50 am.