Lesson 3: 7-3 Graphing Reciprocal Functions

1. A rational expression cannot have zero for a denominator. How does this help determine the asymptote of a hyperbola?
2. What is the domain of a hyperbola?
3. Of what kind of function is a hyperbola a recirprocal?
4. Is it possible for a hyperbola to have more than one nonpermissible value? Explain.

Reciprocal Function
Hyperbola

A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

F.IF.4 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.

F.BF.3 Identify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

SAT questions related to rational functions: 1-3-13, 6-3-12

A reciprocal function has an equation of the form f(x)=1/a(x) where a(x) is a linear function and a(x) does not equal zero. Reciprocal functions may have breaks in continuity for values that are excluded from the domain, and some may have an asymptote, a line that the graph of the function approaches.

The sophomore class is renting an indoor trampoline park for a class party. The cost of renting the facility is $900, which is shared equally among all students who attend. If c represents the cost to each student and n represents the number of students, then c=900/n.

Suggest that students choose a large unit on their grid paper and estimate point coordinates to the nearest tenth. Point out that they may not be able to see the shape of the graph as a whole unless they use a graphing calculator or computer program.

Have students graph one of the functions from the lesson on a large sheet of poster board to clearly show how the graph approaches but never reaches an asymptote. Encourage students to use a variety of colored markers.

McGraw Hill resources

McGraw Hill resources