MAT-145 Survey of Functions I
This course is an introduction to the study of families of functions. Power, piecewise, quadratic, and polynomial functions are covered extensively. Right and non-right trigonometry is also studied in depth. The use of realistic applications and modeling with these families of functions are essential elements of this course. Emphasis on multiple methods of solving equations (algebraic, graphic, and numeric) is included as are multiple representations (algebraic, graphic, numeric, and verbal) of mathematical information. This course carries SUNY General Education approved credit in Mathematics (and Quantitative Reasoning).
Prerequisite
MAT-097 with a C- or higher or Placement into Math Level 2 or Higher
For more detailed course information view the
Course Outline
Course Description
This course is an introduction to the study of families of functions. Power, piecewise, quadratic, and polynomial functions are covered extensively. Right and non-right trigonometry is also studied in depth. The use of realistic applications and modeling with these families of functions are essential elements of this course. Emphasis on multiple methods of solving equations (algebraic, graphic, and numeric) is included as are multiple representations (algebraic, graphic, numeric, and verbal) of mathematical information. This course carries SUNY General Education approved credit in Mathematics (and Quantitative Reasoning).
Credit Hours
3Semester(s) Course Will Be Offered
Fall, Spring, Summer
Prerequisites
MAT-097 with a C- or higher or Placement into Math Level 2 or Higher
SUNY General Education Course
- Mathematics and Quantitative Reasoning
Course Learning Outcomes
- Model realistic scenarios using power, piecewise, quadratic, and exponential functions.
- Solve equations algebraically, graphically, and numerically (via tables) and evaluate the result for reasonableness.
- Use function notation to express mathematical concepts.
- Apply concepts of triangle trigonometry to solve problems.
Topic Outline
- General outline of topics covered:
- 1. Graphing utility usage (embed throughout the course)
- a. Evaluating expressions and functions
- b. Using the table function
- c. Graphing functions
- d. Changing window bounds
- e. Finding key points such as minimums, maximums, intersections, and intercepts
- f. Translating algebraic expressions into calculator input
- g. Solving equations graphically
- h. Expectations for hand-drawn graphs
- i. Labeled axes, proper scale, intercepts, local minimums and maximums, and end behavior
- 2. Concepts common to piecewise, power, quadratic, and polynomial function families (embed throughout the course where appropriate)
- a. Understanding and using function notation, including variables other than x and y
- b. Function evaluation
- c. Characteristics of their graphs
- d. Choosing bounds to graph functions in an appropriate window using a graphing utility
- e. Finding the zeros and vertical intercept algebraically and graphically
- f. Solving graphically for the input of a function given an output
- g. Solving inequalities related to functions graphically
- h. Interpreting the realistic meaning of the inputs and outputs, zeros, and y-intercept
- i. Stating domain and range, both abstract and realistic
- j. Effects (graphical, algebraic, and verbal) of transformations
- k. Defining a formula for a function from a given graph, table, or verbal description
- l. Describing end behavior of functions
- m. Calculating and interpreting average rate of change (AROC)
- 3. Power functions
- a. Direct vs. inverse variation
- b. Definition of negative and rational exponents (and their relationship to radicals)
- c. Simplifying and changing the form of power functions, for example:
- i. Rewriting f(x) = ∛x into f(x) = x¹ᐟ³
- d. Solving equations involving power functions graphically and algebraically
- e. Modeling with power functions
- f. Properties of graphs of power functions
- i. Even vs. odd positive integer exponents
- ii. Even vs. odd negative integer exponents
- iii. Reciprocals of even and odd integer exponents
- 4. Piecewise-defined functions
- a. Evaluating piecewise functions via a formula or graph
- b. Graphing piecewise functions by hand (e.g., absolute value, step, and linear)
- c. Modeling with piecewise functions (including linear, constant, and step functions)
- 5. Quadratic functions
- a. Solving quadratic equations algebraically
- i. Factoring and taking square roots (review)
- ii. Quadratic formula (QF)
- b. Solving applied problems using quadratic equations
- c. Converting between forms of quadratic functions: standard, vertex, and zeros (factored)
- d. Quadratic functions and graphs: finding and identifying the vertex, axis of symmetry, x-intercepts, and y-intercept algebraically and graphically
- e. Modeling with quadratic functions
- 6. Polynomial functions
- a. Terminology of polynomial functions (degree, odd and even)
- b. End behavior as x approaches positive or negative infinity
- c. Finding the zeros (with multiplicity) from a graph or the zeros (factored) form
- d. Modeling with polynomial functions in zeros (factored) form from given conditions: a graph of the function, or given zeros and another ordered pair
- 7. Trigonometry
- a. General triangle properties and terminology (e.g., sum of interior angles and area)
- b. Pythagorean theorem
- c. Finding the sine, cosine, and tangent of an angle in a right triangle
- d. Using sine, cosine, and tangent to find missing sides and angles of a right triangle
- e. Solving first-degree trig equations (sine, cosine, and tangent) for angles between 0° and 180°
- f. Solving applied problems using right-angle trigonometry (including angles of elevation and depression)
- g. Solving non-right triangles using:
- i. The law of sines, including the ambiguous case
- ii. The law of cosines