MATH 1314 Objectives

MATH 1314 College Algebra -- Objectives

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.