# MAT 136 - College Algebra and Trigonometry I Rational exponents; radicals; polynomial long division; rational expressions; solving quadratic equations and inequalities; polynomial functions; absolute value equations and inequalities; complex numbers; operations of functions; inverse functions; properties of exponential and logarithmic functions; trigonometric functions; reference angles; radian measure; graphs of sine, cosine, and tangent; basic trigonometric identities.
**Prerequisite- Corequisite** Prerequisite: MAT 096 Elementary Algebra and Trigonometry or equivalent
Credits: 4
**Hours** 4 Class Hours
**Course Profile** Learning Outcomes of the Course:
Upon successful completion of this course the student will be able to:
Perform skills in three categories: Algebra, Geometry, and Trigonometry.
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 involving radicals and rational exponents.
4. Perform operations and simplify expressions involving complex numbers.
5. Rationalize denominators and numerators.
6. Understand the definition of a function 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 function 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 measured in degrees and radians.
22. Find the trigonometric functions for a general angle.
23. Use reciprocal, Pythagorean, co-function, 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 and inverse trigonometric functions of acute angles and applications of right triangles.
27. Solve logarithmic and exponential equations.
**Graphing:**
28. Identify and graph the following families of relations:
a. ax + by = c
b. y = ax^{2} + bx + c
c. y = x^{n
}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
29. Graph functions and relations by using various graphing techniques: symmetry, reflection, translation and contraction.
30. Sketch a comprehensive graph of a polynomial function including end behavior, extrema and real zeros.
31. Relate the graphs of y = sinx and y = cosx to the unit circle.
32. Graph inverse functions.
33. Graph piece-wise functions.
This course prepares students to meet the Mathematics General Education requirement.
In context of the course objectives listed above, upon successful completion of this course the student will be able to:
1. Interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics.
2. Represent mathematical information symbolically, visually, numerically and verbally.
3. Employ quantitative methods such as arithmetic, algebra, geometry, or statistics to solve problems.
4. Estimate and check mathematical results for reasonableness.
5. Recognize the limitations of mathematical and statistical methods.
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