4.4 Pre-Calculus: Math120

Course Description: Students will explore advanced topics in algebra, including various functions and their graphs and learn the properties of functions, such as the graphs and properties of inverse functions, composite functions, polynomial and rational functions, trigonometry, exponential and logarithmic functions. In addition, students will be able to construct the models for the special occasions or the real-world scenarios. By the end of the course, students should know the following hows:

1) How to find the equation of a line, identify/interpret x and y intercepts and slope of the line

2) How to graph lines, including perpendicular and parallel lines in the x, y-plane

3) How to analyze and solve simple real-world application problems involving linear and quadratic function models

4) How to simplify, evaluate and analyze functions and expressions

5) How to graph common functions, i.e. a parabolic, cubic, square root, linear, reciprocal, identity, exponential function, and etc. as well as how to perform horizontal and vertical transformation, and reflection with respect to the x and y-axis

6) How to obtain information from the graph of a function, such as: stating the domain and range; stating the intervals where the function is increasing, decreasing or is constant; locating any maximum/minimum values; stating intervals where the function is positive or negative; identifying horizontal, vertical and oblique asymptotes; and more

7) How to perform operations on functions including composition, difference quotients, and inverses

8) How to express graphically the behavior of rational functions near asymptotes and at infinity using the concept of the limit

9) How to apply techniques for finding zeros of polynomial functions

10) How to use the unit circle to define the six trigonometric functions

11) How to express angle measurements in degrees and/or radians, of the unit circle as it relates to trigonometric functions, and of right triangle trigonometry

12) How to graph trigonometric functions

13) How to prove trigonometric identities

14) How to apply addition and subtraction, double-angle and half-angle formulas

By Yonghong L McDowell