Calculus Week 7 Rational Functions Graph and Inequalities Questions

Mathematics

Complete the Week 7 Guided Lecture notes document and the other practice docs and answer the following questions

• • Can a quadratic function have a range of all real numbers? Explain.
  • Can the graph of a polynomial function have no y-intercept? Can it have no x-intercepts? Explain.
  • If the graph of a rational function R has the vertical asymptote x=4, the factor x-4 must be present in the denominator of R. Explain why.
  • The graph of a rational function R cannot have both a horizontal and an oblique asymptote. Explain why.
  • Explain the circumstances under which the graph of a rational function will have a hole.
  • Why do we use the test points to graph polynomial or rational function? …To solve a polynomial or rational inequality?

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