2-Day Lesson:

Day 1:

PPT: 22 slides, Annotated PPT: 22 slides, Video: 36 minutes

Day 2:

PPT: 14 slides, Annotated PPT: 14 slides, Video: 24 minutes

Objectives

(Explanation of Standards)

·Find the domain of a rational function using both set-builder and interval notation.

·Identify the domain of a rational function by setting the denominator equal to zero and relating this to the vertical asymptotes and/or holes (discontinuities).

·Define an asymptote as a line that a graph will approach but never touch.

·Identify the asymptotes, domain and range of a reciprocal function from its graph.

·Graph rational functions by hand using a table (for example: y= x/(x+3 )); graph more complicated rational functions using graphing technology.

·Identify vertical asymptotes and/or holes when suitable factorizations are available, and sketch them on the graph.

·Identify a horizontal asymptote by comparing the degrees of the numerator and denominator.

·Find zeros (x-intercepts) of a rational function by setting the numerator equal to zero.

·Understand that a graph has an oblique asymptote when the degree of the numerator is one larger than the degree of the denominator.

·Find the equation of oblique asymptotes by using long division or synthetic division, disregarding any remainders.

·Interpret key features of the graph of a rational function in the context of a real world scenario.

Learning Goal

Learning Goal 14: Students will be able to graph and interpret key features of rational functions.