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
1. identifying the zeros of a polynomial function;
2. generating the linear factors of a polynomial function;
3. generating a polynomial function with given zeros.
Recognize, solve, and apply systems of linear equations using matrices by
1. solving systems of equations using the graphing method, addition method, and/or substitution method;
2. classifying a system as consistent, inconsistent, or dependent;
3. defining a matrix;
4. performing matrix arithmetic;
5. using at least one of the following methods to solve a system of linear equations: matrix inverse method, Cramer’s rule, and row reduction;
6. evaluating a determinant.
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