Class time to complete the Unit 2 Rational Functions Group Task (Assessment)

This assessment is a group task (you may work with up to 3 other people). It will be open notes, and you will be able to use the TI-84 graphing calculators in the classroom.

Rubric for Performance Task (explanations and math practices). Note: this rubric will be used to assess the explanations not the accuracy of the content. Accuracy of content is considered separately.

Graphing Rational Equations: Domain, Range, and Asymptotes

You will be able to identify the general shape of a rational function graph (hyperbola)
You will be able to identify the Vertical and Horizontal Asymptotes of a rational function
You will be able to use Desmos and/or a TI-84 to generate a reasonable graph of a rational function, including
- entering the equation correctly
- using a table of values to find points on the graph
- finding the asymptotes visually and with the table

Note that rational functions can be seen as having the same types of transformations of other functions we have explored. When written in the form $LaTeX: y=\frac{a}{x-h}+k$
- a represents the stretch, and can be used to see if the branches are reflected
- h represents the horizontal shift, and can be used to identify the domain exclusion. The vertical asymptote will always be x = h.
- k represents the vertical shift, and can be used to identify the range exclusion. The horizontal will always be y = k.
When written in the form $LaTeX: y=\frac{ax+b}{cx+d}$ we are going to focus primarily on the asymptotes
- solving the denominator: gives us the equation of the vertical asymptote: $LaTeX: x=\frac{-d}{c}$ (which is also the domain exclusion).
- the ratio of the leading coefficients, $LaTeX: y=\frac{a}{c}$ represents the horizontal asymptote (and the range exclusion).

Homework: None. Prepare for the individual comprehensive assessment tomorrow (Thursday).

Skills you should have mastered -- and which may be included or embedded!

Simplify rational expressions
Multiply and divide rational expressions
Identify the LCD (Lowest Common Denominator) of two or more rational expressions
Add & subtract rational expressions with like denominators (and simplify, if necessary)
Add & subtract rational expresions with unlike denominators
Solve a rational equation by cross multiplying
Solve a rational equation by using the LCD to clear the fractions
Recognize when to use which method most efficiently
Identify extraneous solutions

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Rational Unit Resources Module