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Learning Goal

‹6 of 9 in this skill_area›

Rational functions (asymptotes, domain restrictions)

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Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework

"Make connections between a table, an algebraic representation, or a graph of a: • polynomial function, simple rational function, or quadratic or exponential function that involves a transformation, not in context." "Make connections between a table, an algebraic representation, or a graph of a: • polynomial function, simple rational function, or other nonlinear function in a context, or a quadratic or exponential function that involves a transformation in a context."

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"Make connections between a table, an algebraic representation, or a graph of a: • polynomial function, simple rational function, or quadratic or exponential function that involves a transformation, not in context."
"Make connections between a table, an algebraic representation, or a graph of a: • polynomial function, simple rational function, or other nonlinear function in a context, or a quadratic or exponential function that involves a transformation in a context."

What you'll learn

  1. Describe a simple rational function's graph (domain, vertical asymptotes, holes, horizontal asymptote, and intercepts) from its equation, and match the function to its graph or to a table of values
  2. Determine the domain by excluding the zeros of the *original* denominator, and explain why the function is *undefined* at an excluded value, rather than zero or infinite
  3. Distinguish a vertical asymptote from a hole by whether the responsible factor cancels, state a hole's coordinates, and describe the behavior on each side of a vertical asymptote with a sign or magnitude test
  4. Determine the horizontal asymptote by comparing numerator and denominator degrees
  5. Find the x-intercepts from the numerator's zeros, and the y-intercept as f(0)

Slides

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