# MA.1 - Polynomial and Rational Functions

MA.1  The student will investigate and identify the properties of polynomial, rational, piecewise, and step functions and sketch the graphs of the functions.

### UNDERSTANDING THE STANDARD

·  The graph of polynomial, rational, piecewise, and step functions can be determined by exploring properties of the functions.

·  A variety of notations should be used, including set notation and interval notation.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·  MA.11  Identify a polynomial, rational, piecewise, and step function, given an equation or graph.

·  MA.12  Given a graph or equation of a polynomial, rational, piecewise, or step function, identify:

­  domain and range;

­  zeros;

­  intercepts;

­  symmetry;

­  asymptotes (horizontal, vertical, and oblique/slant);

­  points of discontinuity;

­  intervals for which the function is increasing, decreasing or constant;

­  end behavior; and

­  relative and/or absolute maximum and minimum points.

·  MA.13  Sketch the graph of a polynomial, rational, piecewise, or step function.

·  MA.14  Investigate and verify characteristics of a polynomial, rational, piecewise, and step function, using a graphing utility.

·  MA.15  Rationalize the denominator of a rational function.

### KEY VOCABULARY

Updated: May 29, 2018