Functions:

• Use and interpret function notation.
• Find the domain of polynomial, rational, radical, exponential, and logarithmic functions.
• Use composition of functions.
• Find inverses of functions algebraically (where possible), graphically, and numerically.
• Interpret the graphs of functions.

Graphing functions:

• Recognize the equations and sketch the graphs of the following: Lines, x², x³, x^1/3, x^1/2, 1/x, 1/x², |x|, semi-circles, circles, factored polynomials of degree 3 or more, a^x, log_ax, and their linear transformations.
• Find inverses of functions graphically.
• Find and sketch asymptotes of rational, exponential, and logarithmic functions.
• Describe the end behavior of all the above functions.
• Determine when it is appropriate to use a calculator or graphing technology.
• Approximate zeros of a function.

Symbolic Adeptness:

• Solve equations including quadratic, rational, literal, quadratic types, exponential, logarithmic, and equations with radicals.
• Solve polynomial and rational inequalities.
• Solve non-linear systems of equations.
• Use long division and the Fundamental Theorem of Algebra to find zeros of polynomials of degree three or more.
• Simplify fractions with terms having negative exponents.
• Rationalize numerators as well as denominators.
• Simplify complex fractions.
• Use completing the square to find the vertices of parabolas and centers and radii of circles.
• Evaluate exponential and logarithmic expressions with calculators.
• Use the rules for logarithms.
• Solve systems of linear equations using Gauss-Jordan Elimination and Cramer's Rule.

Applications

• Recognize and use applications of linear functions including linear models.
• Recognize and use quadratic applications, including falling object, maximum, and minimum problems.
• Recognize and use rational expression applications such as animal populations in parks.
• Recognize and use exponential and logarithmic applications, including exponential growth and decay, doubling time, and half-life.
• Recognize and use applications of systems of linear equations.

Last updated January 11, 1999. Louise Hasty