The student will be able to:

1. Read and understand a mathematics textbook.
2. Graph, analyze, and transform polynomial, rational, exponential, logarithmic, and trigonometric functions, and solve and apply related equations and inequalities.
3. Recognize the relationship between functions and their inverses graphically and algebraically.
4. Solve application problems using polynomial, rational, exponential, logarithmic, and trigonometric functions, and model real world applications.
5. Explore circles and angles.
6. Evaluate and simplify trigonometric expressions using identities.
7. Solve right and oblique triangles.
8. Use technology, such as graphing calculators and/or computer software, to assist in solving problems involving any of the topics in (2) through (7) above.
9. Discuss mathematical problems and write solutions in accurate mathematical language and notation.
10. Interpret mathematical solutions.

1. Read and understand a mathematics textbook
   1. Explain mathematical concepts in mathematical language
   2. Explain mathematical concepts in familiar language
   3. Translate mathematical definitions into familiar language
   4. Translate mathematical notation into familiar language
   5. Explain the connections between mathematical concepts
2. Graph, analyze, and transform polynomial, rational, exponential, logarithmic, and trigonometric functions, and solve and apply related equations and inequalities
   1. Recognize each function type
   2. Explore the behavior of graphs
      1. Perform a sign analysis
      2. End behavior
      3. Asymptotes
      4. Increasing and decreasing
      5. Local extrema
   3. Find domain and range
   4. Solve equations and inequalities
3. Recognize the relationship between functions and their inverses graphically and algebraically
   1. Determine whether or not a function has an inverse function
   2. Properties of inverse functions
   3. Notation
4. Solve application problems using polynomial, rational, exponential, logarithmic, and trigonometric functions, and model real world applications
   1. Investigate applications involving functions, such as:
      1. Compound interest
      2. Exponential population models
      3. Radioactive decay
      4. Newton's law of cooling
      5. Interpret amplitude, period, frequency, and shifts within the context of a trigonometric model
5. Explore circles and angles
   1. Convert between degrees and radians
   2. Arc length
   3. The unit circle
   4. Define sine, cosine, tangent, cotangent, cosecant, and secant functions
   5. Evaluate sine, cosine, tangent, cotangent, cosecant, and secant functions at a given angle
6. Evaluate and simplify trigonometric expressions using identities
   1. Pythagorean identity
   2. Odd and even identities
   3. Reciprocal identities
   4. Double angle identities
7. Solve right and oblique triangles
   1. Describe the six trigonometric functions using right triangles
   2. Use the appropriate trigonometric ratio to solve right triangles
   3. Apply the formulas for the Law of Sines and Law of Cosines
8. Use technology, such as graphing calculators and/or computer software, to assist in solving problems involving any of the topics in (2) through (7) above
   1. Calculator/computer utilities for evaluating problems involving optimization
   2. Calculator/computer utilities for finding zeros or roots of functions
9. Discuss mathematical problems and write solutions in accurate mathematical language and notation
   1. Application problems from other disciplines
   2. Proper notation
10. Interpret mathematical solutions
    1. Explain the significance of solutions to application problems

Not applicable.

Written homework
Quizzes and tests
Proctored comprehensive final examination

Lecture
Discussion
Cooperative learning exercises

Boelkins, Matthew. Active Prelude to Calculus. 2019.

Abramsom, Jay. Precalculus, 2nd ed. (Openstax). 2024.

1. Homework problems covering subject matter from text and related material ranging from 20-40 problems per week. Students will need to employ critical thinking in order to complete assignments.
2. Six hours per week of lecture covering subject matter from text and related material. Reading and study of the textbook, related materials, and notes.
3. Student activities covering subject matter from textbook and related materials. Activities will require students to discuss mathematical problems, write solutions in accurate mathematical language and notation, and interpret mathematical solutions.
4. Worksheets: Problems and activities covering the subject matter. Such problems and activities will require students to think critically. Such worksheets may be completed inside and/or outside of class.