# MAT 15x College Algebra Learning Objectives

### Arizona State

• Students will be able to apply algebraic reasoning solve a range of problems.
• Students will develop skills required for success in future studies calculus.

### Arizona Western

Upon satisfactory completion of this course, students will be able to:
2.1 investigate linear functions and use them to model real world data.
2.2 solve algebraic equations and inequalities.
2.3 analyze graphs of functions and transformations of these graphs.
2.4 identify functions and their graphs, and use them to model real world data.
2.5 demonstrate a fundamental understanding of exponential and logarithmic functions.
2.6 demonstrate an understanding of systems of equations and inequalities.
2.7 perform matrix algebra and use matrices to solve systems of equations.
2.8 identify, evaluate, and apply sequences, series, counting principles, and probability.

### MCCCD Official Course Competencies

1. Analyze and interpret the behavior of functions, including end behavior, increasing and decreasing, extrema, asymptotic behavior, and symmetry. (I, II, III)
2. Solve polynomial, rational, exponential, and logarithmic equations analytically and graphically. (I, II, III)
3. Find real and complex zeros of polynomial functions analytically and graphically. (II)
4. Graph polynomial, rational, exponential, logarithmic, power, absolute value, and piecewise-defined functions. (I, II, III)
5. Determine domain and range of polynomial, rational, exponential, logarithmic, power, absolute value, and piecewise-defined functions. (I, II, III)
6. Use transformations to graph functions. (I, II, III)
7. Perform operations, including compositions, on functions and state the domain of the resulting function. (I, II, III)
8. Determine whether a relation is a function when represented numerically, analytically, or graphically. (I, II, III)
9. Determine whether a function is one-to-one when represented numerically, analytically, or graphically. (I, II, III)
10. Determine the inverse of a relation when represented numerically, analytically, or graphically. (I, II, III)
11. Classify functions by name when represented numerically, analytically, or graphically. (I, II, III)
12. Determine regression models from data using appropriate technology and interpret results. (I, II, III)
13. Read and interpret quantitative information when presented numerically, analytically, or graphically. (I, II, III, IV)
14. Justify and interpret solutions to application problems. (I, II, III, IV, V)
15. Compare alternative solution strategies. (I, II, III, IV)
16. Calculate and interpret average rate of change. (I, II, III)
17. Model and solve real world problems. (I, II, III, IV, V)
18. Solve systems of three linear equations in three variables. (IV)
19. Solve systems of linear inequalities. (IV)
20. Communicate process and results in written and verbal formats. (I, II, III, IV, V)

### Northern Arizona University

No learning objective located.

### Pima CC

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:

1. Define a function in terms of ordered pairs, graphically, and algebraically.
2. Determine the domain of a function, and determine whether an element is in the range of a function.
3. Use the algebra of functions and composition of functions defined by the modes in objective.
4. Use the definition of a one-to-one function and compute the inverse of a one-to-one function.
5. Define and calculate, exactly and by approximation, zeros and intercepts of functions.
6. Perform basic operations with complex numbers.
7. Find the zeros of polynomial functions by approximation and using simple algebraic methods.
8. Given its zeros and their multiplicities, construct a polynomial function and sketch its graph.
9. Graph rational functions.
10. Solve nonlinear inequalities graphically.
11. Use the properties of exponential functions.
12. Use the concept of inverse functions to develop and work with logarithmic functions.
13. Solve exponential and logarithmic equations.
14. Solve applications, by algebraic means and by approximation, using polynomial, single radical, power, rational, exponential, and logarithmic functions.
15. Solve application problems using linear systems.
16. Use graphing calculators (or other technology).
17. Using technology to model data (linear regression).

### University of Arizona

• To promote problem-solving and critical thinking skills through the application of algebraic concepts to common situations
• To enhance the understanding of algebraic concepts through the integrated use of graphing technology in the curriculum
• To utilize and promote the “Rule of Four” – every topic should be presented algebraically, graphically, numerically, and in context with applications
• To incorporate writing into the curriculum
• To provide a sufficient algebra background to prepare students for Math 113, Math 116, and Math 163/263
• To help strengthen students’ general academic skills
• Note that more detailed objectives are listed in the Class Notes packet that can be obtained in the university bookstore

### Yavapai

1. Use technology to recognize trends in data. (1,2,3,4,6) (QL1-4)
2. Create suitable functions that model data using technology. (1,2,3,4,6) (QL 1-3)
3. Analyze an application using a function developed from data. (1,2,3,4,6) (QL 1-4)
4. Add, subtract and multiply matrices in the context of an application. (5,6) (QL 1,2,4)
5. Solve a system of equations using matrices and technology. (5,6) (QL 1,2)