MATH& 141

Precalculus I

LEARNING OUTCOMES

Upon successful completion of Math& 141, the student should be able to:

1. Simplify algebraic, exponential and radical expressions.
2. Solve linear equations and inequalities.
3. Graph linear equations.
4. Solve absolute value, non-linear and rational inequalities.
5. Simplify complex fractions.
6. Factor expressions and solve equations containing negative and fractional exponents.
7. Identify functions from algebraic, graphical, tabular and verbal representations. Use function notation when evaluating functions and sketching graphs of functions.
8. Identify domain and range of functions.
9. Graph a piece-wise defined function.
10. Identify properties of graphs such as relative and global maximum and minimum, symmetry, increasing, decreasing, even, and odd.
11. Translate the graph of a function.
12. Translate the graph of a circle in standard or general form.
13. Solve application problems and interpret, and draw inferences from, the results.
14. Analyze and graph quadratic functions by hand and using a graphing calculator.
15. Find the equations of quadratic functions from given data.
16. Set up and solve quadratic applications, including maximum/minimum problems.
17. Perform operations on functions, including composition of functions.
18. Identify one-to-one functions.
19. Identify, analyze and graph the inverse of a function. Find the inverse of a given function.
20. Analyze and graph polynomials functions of degree greater than 2.
21. Divide two polynomial functions.
22. Apply the Remainder Theorem and Factor Theorem.
23. Perform basic operations on complex numbers.
24. Find real and complex zeros of polynomials.
25. Use a calculator to assist in finding real zeros of polynomials.
26. Graph rational functions.
27. Analyze and graph exponential and logarithmic functions
28. Solve exponential and logarithmic equations.
29. Set up and solve exponential and logarithmic application problems.
30. Solve a non-linear system of equations.
31. Solve a system of linear equations using matrices and a graphing calculator.
32. Set up and solve application problems using a system of equations.