Florida B.E.S.T. MA.912.AR.8

MA.912.AR.8 is a B.E.S.T. standard. These are the benchmarks under it.

• MA.912.AR.8.1

  Write and solve one-variable rational equations. Interpret solutions as viable in terms of the context and identify any extraneous solutions.

• MA.912.AR.8.2

  Given a table, equation or written description of a rational function, graph that function and determine its key features.

• MA.912.AR.8.3

  Solve and graph mathematical and real-world problems that are modeled with rational functions. Interpret key features and determine constraints in terms of the ...

01

What Students Need to Do

Students find values that make rational equations true while tracking values that make denominators zero. They graph rational relationships using intercepts, holes, asymptotes, domain restrictions, and end behavior.

02

What Mastery Looks Like

Students find valid solutions and reject values that make a denominator zero. They sketch rational graphs with accurate intercepts, holes, asymptotes, and end behavior. They connect equations, tables, and graphs.

03

Common Misconceptions

Students cancel terms across addition instead of canceling common factors. They keep excluded values as solutions after clearing denominators. They may label every denominator zero as an asymptote, even when a canceled factor creates a hole.

04

How to Assess It

Exit ticket: For f(x)=(x²−1)/(x−1), state the restriction, identify any hole, and sketch the graph. Then solve 2/(x−1)=3/(x+2) and check the solution.

1. 01

   Use yarn for asymptotes and sticky dots for intercepts and holes, then sketch y=(x+1)/(x−2) on chart paper.

2. 02

   Ask students to explain why canceling x in (x+2)/x is invalid, while canceling x in 2x/x is valid.

3. 03

   Run a card sort matching rational formulas with domain restrictions, asymptotes, holes, intercepts, and graph sketches.

4. 04

   Model average cost with A(x)=(500+8x)/x, then graph it and explain what happens as production increases.

• MA.912.AR.3

  Write, solve and graph quadratic equations, functions and inequalities in one and two variables.

• MA.912.AR.7

  Solve and graph radical equations and functions in one and two variables.

• MA.912.AR.6

  Solve and graph polynomial equations and functions in one and two variables.

• MA.912.AR.2

  Write, solve and graph linear equations, functions and inequalities in one and two variables.