Evidence of Understanding

**describe connections between a rational equation and the features of its graph**- describe the general shape and patterns for the graph of a
**rational function**including domain, range, end behavior, and**asymptotes** - use the equation to justify vertical asymptotes on the graph (limits on the domain)
*possible extension: use the degree of the numerator and denominator of the rational function to predict**oblique asymptotes**and use long division to determine their equations*

- use the structure of an equation to identify ways to rewrite it and determine asymptotes (mainly via factoring but possibly also applying properties of polynomials)

- describe the general shape and patterns for the graph of a
**solve rational functions in the context of a situation**- build equations that model the relationship between two variables in a rational function
- connect equivalent mathematical representations (an equation to a situation, etc.) and justify the connection
- use multiple mathematical representations (equation, table, graph) to uncover solutions to a problem or answer questions for a given situation
- rewrite rational expressions in different forms using long division when necessary
*Example:*^{(x+4)}/_{(x+3)}=^{(x+3) +1}/_{(x+3)}= 1 +^{1}/_{(x+3)}*Example:*^{(x3 + 5x2 + 3x - 2)}/_{(x + 1)}= x^{2}+ 6x + 9 +^{7}/_{(x + 1) }

- solve rational equations and verify
**extraneous solutions**

Develop conceptual understanding:

rational function, asymptote, extraneous solution, *(+)oblique asymptote*

Supporting terms to communicate:

domain, range, end behavior, degree, polynomial, roots, zeros, variable, term, binomial factor