CCSS.Math.Content.HSF-IF.C.7d
The standard
(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
Common Core State Standards for Mathematics · Analyze functions using different representations
What this standard means
Students need to graph rational functions from factored forms. They should find zeros from the numerator, vertical asymptotes from denominator factors, and holes when factors cancel. They also need to describe what happens far left and far right, using degree comparisons or division when needed.
Mastery looks like a clean graph with labeled intercepts, asymptotes, holes, and correct branch behavior near each asymptote. Students often mix up zeros and vertical asymptotes, forget holes, or draw branches crossing asymptotes. They also struggle when a horizontal asymptote is not enough to show end behavior clearly.
Ways to teach it
- Give pairs six factored rational functions, graph paper, and colored pencils to mark zeros, asymptotes, holes, and final branches.
- Ask students to explain why x equals 3 can be a zero, a vertical asymptote, or a hole depending on the factors.
- Use an exit ticket with one factored rational function and ask for zeros, vertical asymptotes, holes, and end behavior only.
- Connect rational graphs to average cost, using C(x) divided by x to show how cost per item levels off as production grows.
Plan a lesson for CCSS.Math.Content.HSF-IF.C.7d
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Related standards
- CCSS.Math.Content.HSA-APR.B.3
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial...
- CCSS.Math.Content.HSF-IF.C.8a
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in ...
- CCSS.Math.Content.HSF-IF.C.7c
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
- CCSS.Math.Content.HSA-SSE.B.3a
Factor a quadratic expression to reveal the zeros of the function it defines.