Syllabus for College Algebra

1. Identify the characteristics of a quadratic function (i.e., vertex, axis of
symmetry, and direction of concavity).
2. Compute roots/zeroes of a polynomial function by factoring techniques.
3. Estimate the roots/zeroes of a polynomial function.
4. Solve polynomial inequalities.
5. Solve systems of linear equations using matrices and determinants.
6. Solve systems of linear inequalities.
7. Solve systems of non-linear equations.

Rational Functions and Models

8. Simplify rational expressions using the division algorithm .
9. Identify points of discontinuity of a rational function.
10. Identify vertical/horizontal asymptotes and end behavior of rational functions.
11. Solve rational inequalities.

Power Functions and Models

12. Solve radical equations and equations with fractional exponents.
13. Identify the domain, range of power functions; determine if the function has an
inverse. Find the inverse and its domain and range, if appropriate.

Exponential and Logarithmic Functions and Models

14.Define exponential and logarithmic functions.
15. Simplify exponential and logarithmic expressions using their properties
16. Solve exponential and logarithmic equations.
17. Formulate and apply exponential and logarithmic functions to a contextual
situation.

It is expected that the following student learning outcomes
(Characteristics of Functions) will be embedded as appropriate in the study
of the family of functions listed above.

• Identify the domain and range of a function.
• Determine intervals on which functions are decreasing/increasing,
continuous/non-continuous, or piecewise.
• Identify functions from multiple sources of information (i.e., verbal descriptions,
graphs, equations, and tables of values ).
• Relate the effect of transformations (i.e., translations, rescaling, or reflections)
on graphs of functions and their corresponding equations.
• Perform operations (i.e., addition, subtraction, multiplication and division) on
functions, including the composition of functions.
• Decompose a function into a composition of two or more functions .
• Formulate and apply a function to a contextual situation.
• Determine the conditions under which a function has an inverse.
• Identify the inverse of a function from multiple representations.
• Reformulate a given function into various representations (i.e., verbal,
graphical, algebraic, or tabular).