Course Number and Title: MAT 183 Reasoning with Functions I
Reasoning with Functions I is the first course of a two course sequence that prepares students to enter Calculus and be successful in future STEM coursework. This course will focus on functions by examining multiple representations and explicit covariational reasoning to investigate and explore quantities, their relationships, and how the relationships change. In addition, students taking the course will analyze a variety of function types including linear, quadratic, polynomial, power, exponential, and logarithmic.
- Investigate quantities, describe and connect relationships between quantities, and attend to how two quantities change together using multiple representations of different function types. (CCC 2,6)
- Analyze and solve contextualized problems by converting between different representations and algebraic forms of functions and connecting common characteristics or features between those functions. (CCC 2,6)
- Apply algebraic reasoning to write equivalent expressions, solve equations, and interpret inequalities. (CCC 2,6)
See Core Curriculum Competencies and Program Graduate Competencies at the end of the syllabus. CCPOs are linked to every competency they develop.
Upon completion of this course, the student will:
- Investigate quantities, describe and connect relationships between quantities, and attend to how two quantities change together using multiple representations of different function types.
- Conceptualize and define variables that are present in a given situation to include: measurement and association of units within numerical values and “delta” notation to denote change in quantities.
- Compare and interpret how two quantities change together by justifying the presence of a relationship, identifying constraints on quantities and domains, distinguishing between dependent and independent variables, and drawing diagrams of situations.
- Interpret rates of change of quantities embedded in multiple representations (e.g. tables, graphs, contexts, and equations) to include: constant rate of change, average rate of change, and intuitive treatments of instantaneous rates of change.
- Utilize function notation where necessary and make sense of how the inputs and outputs are related to the given situation.
- Investigate, connect, and describe the patterns and relationships found in multiple function types to include: linear, quadratic, exponential, logarithmic, rational, periodic, piecewise, and absolute value functions.
- Analyze and solve contextualized problems by converting between different representations and algebraic forms of functions and connecting common characteristics or features between those functions.
- Create, use, and interpret linear equations and convert between forms as appropriate to include: reading slope and intercept from multiple representations; calculate equations of lines given the point and slope, two points, or statements about proportional relationships and/or first differences being constant..
- Create, use, and interpret exponential equations and convert between forms as appropriate to include: modeling constant percent change, half-life, doubling time, similarities to linear, rate of change is exponential, rate of change is proportional to the amount, the role of e, describing long-term behavior, inverting the exponential process (logarithms).
- Construct, use, and describe transformations and operations of functions to include: operations of functions, vertical and horizontal shifts and stretches.
- Construct, use, and describe compositions of functions to include: how composition of functions can be used to generate other important functions, how composition of functions transmits variation.
- Construct, make sense of, use, and describe inverses of functions to include: roots (radicals) and logarithms.
- Apply algebraic reasoning to write equivalent expressions, solve equations, and interpret inequalities.
- Simply expressions and locate roots using factoring techniques to include: the distributive property, multiplication of polynomials, completing the square, work with inequalities
- Simplify a variety of expressions and find roots of equations involving multiple function types to include: facility with rules for exponents and logarithms; polynomial, power, radical, and rational functions; asymptotic behavior of functions near roots of the denominator as s increases/decreases without bound.
The grade will be determined using the Delaware Tech grading system:
Students should refer to the Student Handbook for information on the Academic Standing Policy, the Academic Integrity Policy, Student Rights and Responsibilities, and other policies relevant to their academic progress.
Calculated using the following weighted average
Percentage of final grade
Exams – 3 Unit tests and final
- Apply clear and effective communication skills.
- Use critical thinking to solve problems.
- Collaborate to achieve a common goal.
- Demonstrate professional and ethical conduct.
- Use information literacy for effective vocational and/or academic research.
- Apply quantitative reasoning and/or scientific inquiry to solve practical problems.
The College is committed to providing reasonable accommodations for students with disabilities. Students are encouraged to schedule an appointment with the campus Disabilities Support Counselor to request an accommodation needed due to a disability. A listing of campus Disabilities Support Counselors and contact information can be found at the disabilities services web page or visit the campus Advising Center.