Course goals and learning outcomes support the Foundational Component Areas defined by the Texas Higher Education Coordinating Board. Course goals are linked to the respective Core Curriculum Competencies: Critical Thinking Skills, Communication Skills, and Empirical and Quantitative Skills. Specific competencies are identified in designated course goals and learning outcomes.

Upon successful completion of this course, students will:

Demonstrate and apply knowledge of properties of functions, including domain and range, operations, compositions, and inverses by
1. defining a function;
2. identifying the domain and range of a function;
3. defining odd and even functions;
4. identifying basic functions;
5. detecting and applying transformations of functions;
6. combining functions arithmetically;
7. producing the composition of two functions;
8. identifying one to one functions;
9. producing the inverse of a function;
10. stating and interpreting graphical data;
11. understanding and using piecewise functions;
12. finding and simplifying a function’s difference quotient.
Recognize and apply polynomial, rational, radical, exponential, and logarithmic functions, and solve related equations by
1. applying quadratic functions;
2. solving quadratic inequalities;
3. identifying polynomial functions;
4. defining a rational function;
5. solving equations containing rational exponents;
6. identifying the domain of a rational function;
7. identifying the asymptotes of a rational function;
8. defining an exponential function;
9. defining e;
10. applying exponential functions;
11. defining a logarithmic function;
12. converting between logarithmic form and exponential form;
13. evaluating logarithmic expressions;
14. stating the properties of logarithms;
15. applying the properties of logarithms;
16. solving exponential equations;
17. solving logarithmic equations;
18. solving radical equations;
19. identifying the domain of a radical function;
20. solving problems involving exponential growth and decay.
Apply graphing techniques by
1. producing the graph of a quadratic function;
2. describing the end behavior of a polynomial function;
3. generating a sketch of the graph of a polynomial function;
4. generating the graph of a rational function;
5. generating the graph of an exponential function;
6. generating the graph of a logarithmic function;
7. generating the graph of a radical function;
8. generating the graph of a piecewise function.
Evaluate all roots of higher degree polynomial and rational functions by
Recognize, solve, and apply systems of linear equations using matrices by
Examine sequences and series by
1. defining a mathematical sequence;
2. defining a mathematical series;
3. applying sequences and series.
Critical Thinking Skills: Demonstrate the ability to evaluate, synthesize, and perform inquiry and analysis of information in mathematical problems by
1. distinguishing between the different types of functions;
2. identifying characteristics of functions.
Communication Skills: Demonstrate the ability to communicate orally, visually, and/or in writing using mathematical language and symbols by
1. analyzing and interpreting graphs;
2. illustrating the solution steps to solve equations and/or systems of equations.
Empirical and Quantitative Skills: Manipulate and analyze numerical data or observable facts in making informed conclusions by
1. evaluating functions;
2. writing and solving equations for application problems.

MATH 1314

Download as PDF

MATH 1314 - Corequisite College Algebra