MAT 136 - College Algebra and Trigonometry I

Upon successful completion of this course the student will be able to:
Perform skills in three categories:  Algebra, Geometry, Trigonometry; Non Calculator Graphing; and Graphing Calculator.

Note:  Throughout the course the students are expected to solve applied problems related to the topics of the course.

Algebra, Geometry, Trigonometry:
1.  Perform arithmetic operations and simplification of rational expressions including complex fractions.
2.  Solve absolute value linear equations and inequalities using analytic methods.
3.  Perform operations and simplify expressions involvinig radicals and rational exponents.
4.  Perform operations and simplify expressions involving complex numbers.
5.  Rationalize denominators and numerators.
6.  Understand the definition of a funtion of x and find the domain and range of a function.
7.  Use function notation.
8.  Review linear functions and their applications.
9.  Perform operations on functions including composition.
10.  Find an inverse funtion algebraically.
11.  Use properties of exponential and logarithmic functions.
12.  Use the change of base formula.
13.  Use interval notation.
14.  Solve compound inequalities.
15.  Perform polynomial long division.
16.  Solve quadratic equations and inequalities and applications thereof.
17.  Apply the Remainder Theorem and Factor Theorem to higher degree polynomials.
18.  State the Fundamental Theorem of Algebra and find all complex zeros of a polynomial function.
19.  Construct an expression for a polynomial given its roots.
20.  Use radians to measure angles.
21.  Find reference angles for angles measureed in degrees and radians.
22.  Find the trigonometric funtions for a general angle.
23.  Use recriprocal, Pythagorean, cofunction, quotient and odd/even identities.
24.  Use the distance and midpoint formulas.
25.  Find the arc length and area for a sector of a circle.
26.  Review trigonometric functions of acute angles and applications of right triangles.

Non Calculating Graphing:
27.  Identify and graph the following families of relations:
             a.  ax + by = c
             b.  y = ax² + bx + c
             c.  y = xⁿ
                 d.  y=|x|
             e.  y=¹/_x
             f.  y = a^x
             g.  y = a sin bx
             h.  y = a cos bx
             i.  y = a tan bx
28.  Graph functions and relations by using various graphing techniques:  symmetry, reflection, translation and contraction.
29.  Sketch a comprehensive graph of a polynomial function including end behavior, extrema and real zeros.
30.  Relate the graphs of y = sinx and y = cosx to the unit circle.
31.  Graph inverse functions.
32.  Graph piece-wise functions.

Graphing Calculator:
33.  Graph piece-wise functions.
34.  Plot points and fit a line to the data using calculator regression.
35.  Solve functional and relational inequalities by graphing.
36.  Find roots of polynomials using the zero command.
37.  Solve equations using the zero and the intersection methods.
38.  Solve an equation using the computer algebra system.
39.  Use the Exact and Approximate output mode.
40.  Setup and read tables.
41.  Find minia and maxima using the Math options for the graph.
42.  Get an appropriate window and accurately sketch the graph of a relation or function.
43.  Establish a trigonometric identity by using graphing and using the computer algebra system.
44.  Use the trigonometric and inverse trigonometric commands.
45.  Use the exponential and logarithmic commands.