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, x1/3, x1/2, 1/x, 1/x2, |x|,
semi-circles, circles, factored polynomials of degree 3 or more, ax,
logax, 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.
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Last updated
July 28, 2004
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