Learning Objectives, MAT119: Pre-Calculus

The student will know the properties of elementary functions that are needed to have a reasonable expectation of success in Calculus I. In particular, the student
  1. will be able to identify whether or not a relation is a function and will be able to identify transformations of elementary functions, including shifting, reflecting, and stretching or shrinking.
  2. will be able to combine and compose elementary functions, determine whether an elementary function is injective, and find the inverse of an invertible elementary function.
  3. will be able to model using polynomial and rational functions, determine the intercepts of polynomial functions, and determine the intercepts and asymptotes of rational functions.
  4. will be able to use the properties of exponential and logarithmic functions and will understand that exponentiation and taking the logarithm are inverse operations.
  5. will be able to solve exponential and logarithmic equations.
  6. will understand the definitions of the trigonometric functions defined based upon right triangles or defined based upon points on the unit circle.
  7. will be familiar with the graphs of the trigonometric functions and will understand the concepts of period and amplitude.
  8. will understand degree and radian measure and the relationship between the two systems of angle measure.
  9. will be able to solve right triangles and to apply the Law of Sines and the Law of Cosines.
  10. will be able to prove and use basic trigonometric identities.
  11. will understand the construction of the inverse trigonometric functions and be familiar with their graphs.
  12. will be able to solve trigonometric equations.

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