# MAT 18x Precalculus Learning Objectives

### MCCCD

1. Find real and complex zeros of polynomial functions. (I-II)
2. Calculate and interpret average rate of change. (I-III)
3. Determine the inverse of a relation when represented numerically, analytically, or graphically. (I-IV)
4. Analyze and interpret the behavior of functions, including domain and range, end behavior, increasing and decreasing intervals, extrema, asymptotic behavior, and symmetry. (I-V)
5. Determine whether a function is one-to-one when represented numerically, analytically, or graphically. (I-V)
6. Determine whether a relation is a function when represented numerically, analytically, or graphically. (I-V)
7. Graph polynomial, rational, exponential, logarithmic, power, absolute value, piecewise-defined, and trigonometric functions. (I-V)
8. Perform operations, including compositions, on functions and state the domain of the resulting function. (I-V)
9. Solve polynomial, rational, exponential, logarithmic, and trigonometric equations analytically and graphically. (I-V)
10. Use transformations to graph functions. (I-V)
11. Communicate process and results in written and verbal format. (I-IX)
12. Compare alternative solution strategies. (I-IX)
13. Justify and interpret solutions to application problems. (I-IX)
14. Model and solve real-world problems. (I-IX)
15. Read and interpret quantitative information when presented numerically, analytically, or graphically. (I-IX)
16. Find and evaluate inverse trigonometric functions. (IV-V)
17. Use the definition and properties of trigonometric functions and formulas to solve application problems. (IV-VII)
18. Verify trigonometric identities. (VI)

### Pima CC

Precalculus I Student Learning Outcomes:

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

1. Define functions and determine the domain and range. Perform operations on functions.
2. Solve various types of equations and systems.
3. Graph functions and inequalities.
4. Solve problems involving real world applications.

Performance Objectives:

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

2. Define a function by ordered pairs, a graph, and algebraically; use function operations and inverses; use transformations and determine symmetry.
3. Graph polynomial and rational functions; predict the nature of the zeros of a quadratic function, and reconstruct a polynomial from its given zeros.
4. Solve polynomial, rational, and absolute value inequalities.
5. Graph exponential and logarithmic functions; solve exponential and logarithmic equations; and use curve fitting for explanation of arithmetic models.
6. Understand end-behavior of a function in the context of limits.
7. Solve linear systems algebraically, graphically, and using matrices; solve nonlinear systems graphically and algebraically.
8. Use a graphing calculator to graph and analyze functions.

Precalculus II Student Learning Outcomes:

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

1. Solve trigonometric equations and verify trigonometric identities.
2. Graph trigonometric functions, polar equations, and conic sections.
3. Solve triangles and real world applications.
4. Analyze sequences and series.

Performance Objectives:

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

1. Convert between radians and degrees measures; define, graph, and evaluate the six trigonometric functions and their inverses; solve trigonometric equations algebraically; and use trigonometric identities to simplify expressions and solve equations.
2. Use the standard equations for conic sections and sketch their graphs; identify types of conic sections and determine their features.
3. Graph polar equations; convert between rectangular and polar coordinates; obtain polar form of complex numbers and convert between the polar form and the standard form.
4. Perform calculations involving vectors, including addition, scalar multiplication, finding magnitude, conversions between rectangular and polar form, and applications.
5. Find the nth term of a sequence; calculate partial sums of arithmetic and geometric sequences; and use the Binomial Theorem to expand powers of binomials.
6. Use a graphing calculator to evaluate, graph, and analyze functions.