MATH 1314 College Algebra --
Objectives
Functions:
- Use and interpret functional
notation.
- Find the domain of
polynomial, rational, radical, exponential, and logarithmic functions.
- Find a symbolic
representation of the sum, difference, product, quotient, and composition
of two functions.
- Evaluate the sum, difference,
product, quotient, and composition of two functions at a given value of
the respective domain for functions represented symbolically, graphically,
and numerically.
- Find the inverse of a function
represented symbolically, graphically, or numerically.
- Interpret the graphs of
functions.
Graphing functions:
- Sketch the graphs of the
following functions: Lines, x2, x3, x1/2,
1/x, 1/x2, |x|, factored polynomials of degree 3 or more, ax,
logax, and rigid transformations of these functions.
- Describe the end behavior of
polynomial functions.
- Approximate the zeros of a
function from its graph.
- Solve an inequality involving
a function from its graph.
- Graph a piece-wise defined
function.
Symbolic Adeptness:
- Solve polynomial, rational,
exponential, and logarithmic equations symbolically.
- Solve equations involving
radicals symbolically.
- Solve equations with rational
exponents symbolically.
- Solve equations with negative
exponents symbolically.
- Solve polynomial and rational
inequalities symbolically.
- Use the Fundamental Theorem
of Algebra and the Conjugate Zeros Theorem to find zeros of polynomials of
degree three or greater.
- Find the vertex of a parabola
and the center and radius of a circle by completing the square.
- Find the vertex of a parabola
written in standard form by using the formula h = -b/2a.
- Convert an exponential
equation to logarithmic form, and a logarithmic equation to exponential
form.
- Evaluate exponential and
logarithmic functions using the change of base formula and a calculator.
- Use the properties of
logarithms to expand a logarithmic expression, and to write an expanded
logarithmic expression as a single logarithm.
- Solve a system of linear
equations using Gaussian elimination.
- Solve a system of linear
equations using matrix inversion or Cramer’s Rule.
Applications
- Recognize and use
applications of linear functions.
- Recognize and use
applications of quadratic functions, including falling object problems and
extremum problems.
- Recognize and use
applications of exponential and logarithmic functions, including
exponential growth and decay, doubling time, and half-life problems.
- Recognize and use
applications of systems of linear equations.