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, x^1/2, 1/x, 1/x², |x|, factored polynomials of degree 3 or more, a^x, log_ax, 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.