Upon successful completion of this course, the student will be able to:

• Relations and Functions
  • Distinguish between relations and functions.
  • Evaluate functions both numerically and algebraically.
  • Determine the domain and range of functions in general, including root and rational functions.
  • Perform arithmetic operations on functions, including the composition of functions and the difference quotient.
  • Identify and graph linear, absolute value, quadratic, cubic, and square root functions and their transformations.
  • Determine and verify inverses of one-to-one functions.

• Polynomial and Rational Functions
  • Determine the general and standard forms of quadratic functions.
  • Use formula and completing the square methods to determine the standard form of a quadratic function.
  • Identify intercepts, vertex, and orientation of the parabola and use these to graph quadratic functions.
  • Identify zeros (real-valued roots) and complex roots, and determine end behavior of higher order polynomials and graph the polynomial, and graph.
  • Determine if a function demonstrates even or odd symmetry.
  • Use the Fundamental Theorem of Algebra, Rational Root test, and Linear Factorization Theorem to factor polynomials and determine the zeros over the complex numbers.
  • Identify intercepts, end behavior, and asymptotes of rational functions and graph.
  • Solve polynomial and rational inequalities.
  • Interpret the algebraic and graphical meaning of equality of functions (f(x) = g(x)) and
    inequality of functions (f(x) > g(x))

• Exponential and Logarithmic Functions
  • Identify and graph exponential and logarithmic functions and their transformations.
  • Use properties of logarithms to simplify and expand logarithmic expressions.
  • Convert between exponential and logarithmic forms and demonstrate an understanding of the relationship between the two forms.
  • Solve exponential and logarithmic equations using one-to-one and inverse properties.
  • Solve application problems involving exponential and logarithmic functions.

• Systems of Equations
  • Solve three variable linear systems of equations using the Gaussian elimination method.

• Trigonometric Functions
  • Identify angles in standard form in both degree and radian format and convert from one to the other.
  • Find the arc length.
  • Find the value of trigonometric functions of common angles without a calculator using the unit circle and right triangle trigonometry.
  • Use reference angles to evaluate trig functions.
  • Find the value of trigonometric functions of angles using a calculator.
  • Use fundamental trigonometric identities to simplify trigonometric expressions.
  • Graph the six trigonometric functions using the amplitude, period, phase and vertical shifts.
  • Use trig functions to model applications in the life and natural sciences.

• Analytic Trigonometry
  • Use the fundamental, quotient, Pythagorean, co-function, and even/odd identities to verify trigonometric identities.
  • Use the sum and difference, double angle, half-angle formulas to evaluate the exact values of trigonometric expressions.
  • Determine exact values of expressions, including composite expressions, involving inverse trigonometric functions.
  • Solve trigonometric equations over restricted and non-restricted domains.

• Applications of Trigonometry
  • Solve right triangles and applications involving right triangles.
  • Use the Law of Sines and Cosines to solve oblique triangles and applications.

• Conics
  • Identify the conic sections of the form:Ax^2+By^2+Dx+Ey+F=0.
  • Write the equations of circles, parabolas, ellipses, and hyperbolas in standard form centered both at the origin and not at the origin.
  • Identify essential characteristics unique to each conic
  • Graph equations in conic sections, centered both at the origin and not at the origin.
  • Solve applications involving conic sections.

•  Sequences and Series (Optional unit at the discretion of the department. Not required for transfer.)
  • Identify the terms of geometric sequences.
  • Find a particular term of geometric sequence.
  • Determine the formula for the an term of geometric sequences.
  • Find the sum of first n terms of finite geometric series.
  • Find the sum of infinite geometric series.
  • Introduce arithmetic concepts as time allows.