October 26, 2007

This lesson has students compare and contrast differences between rational functions to understand vertical asymptotes, horizontal asymptotes, and removable and non removable discontinuities.

- Mathematics > General
- Mathematics > Calculus
- Mathematics > Equations
- Mathematics > Graphing

- Grade 9
- Grade 10
- Grade 11
- Grade 12

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.?

Graph linear and quadratic functions and show intercepts, maxima, and minima.

Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).