Upon completing the course, the student will be able to:

Relations and Functions

• Distinguish between relations and functions.
• Evaluate functions both numerically and algebraically.
• Determine the domain and range of functions in general, including root and rational functions.
• Perform arithmetic operations on functions, including the composition of functions and the difference quotient.
• Identify and graph linear, absolute value, quadratic, cubic, and square root functions and their transformations.
• Identify and graph piece-wise defined functions.
• Determine and verify inverses of one-to-one functions.

Polynomial and Rational Functions

• Determine the general and standard forms of quadratic functions.
• Use formula and completing the square methods to determine the standard form of a quadratic function.
• Identify intercepts, vertex, and orientation of the parabola and use these to graph quadratic functions.
• Identify zeros (real-valued roots) and complex roots, and determine end behavior of higher order polynomials and graph the polynomial, and graph.
• Determine if a function demonstrates even or odd
• Use the Fundamental Theorem of Algebra, Rational Root test, and Linear Factorization Theorem to factor polynomials and determine the zeros over the complex numbers.
• Identify intercepts, end behavior, and asymptotes of rational functions, and graph.
• Solve polynomial and rational inequalities.
• Interpret the algebraic and graphical meaning of equality of functions (f(x) = g(x)) and inequality of functions (f(x) > g(x))

Exponential and Logarithmic Functions

• Identify and graph exponential and logarithmic functions and their transformations.
• Use properties of logarithms to simplify and expand logarithmic expressions.
• Convert between exponential and logarithmic forms and demonstrate an understanding of the relationship between the two forms.
• Solve exponential and logarithmic equations using one-to-one and inverse properties.
• Solve application problems involving exponential and logarithmic functions.

Systems of Equations

• Solve three variable linear systems of equations using the Gaussian elimination method.