OBJECTIVES: Upon completion of Math 108, the student should be able to

• Set up algebraic models (equations or inequalities) for various phenomena, solve, and eliminate solutions which are invalid in the context (including but not limited to linear models.)
• Solve inequalities involving absolute value, represent their solutions as intervals, and graph the solutions.
• Perform algebraic operations on polynomial and rational functions, and factor polynomials (as a tool for solving polynomial and rational equations, not an end in itself.)
• Use polynomial long division as necessary to simplify expressions. (Synthetic division is optional.)
• Solve algebraic equations and inequalities, including expressions involving radicals.
• Determine intervals where polynomial and rational functions are positive and negative.
• Understand the relationship between zeros and linear factors of a polynomial; use the rational root theorem.
• Demonstrate understanding of the function concept and the related concepts of domain and range.
• Quickly recall and sketch the graphs of the functions f(x) = x², f(x) = x³, f(x) = 1/x, f(x) = 1/x², f(x) = |x|, f(x) = x^1/2, f(x) = x^1/3, etc.
• Recognize and use symmetry in graphing equations.
• Recognize and use the effects of shifts, reflections and scaling on a graph.
• Graph polynomial and rational functions showing intercepts and horizontal and vertical asymptotes.
• Compute the composition of two functions; recognize a given function as a composition of other functions.
• Demonstrate an understanding of the concepts of one-to-one functions and inverse of a function.
• Compute the inverse of a function and its domain and range; sketch the graph of the inverse of a given function.
• Quickly recall and sketch the graphs of basic exponential and logarithmic functions.
• Solve exponential equations using one-to-one property of exponential functions and /or using logarithms.
• Use the laws of logarithms to simplify logarithmic expressions and to solve logarithmic equations.
• Convert equations from logarithmic to exponential form and vice versa.
• Find the key features of a parabola or circle given its equation.
• Derive the equation of a parabola or circle given its key features or a graph.