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Big Ideas Math Integrated III
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Big Ideas Math Integrated III View details
2. Graphing Rational Functions
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Exercise 2 Page 313

Graph f(x)= 1x and write a some of its characteristics. Notice that zero is neither in the domain nor in the range.

See solution.

Practice makes perfect

Let's begin by graphing the parent rational function f(x) = 1x.

From the graph above we can write some characteristics of the rational functions.
  • We have that f(x)= 1x→ 0 as x→ ∞ and as x→ - ∞. Thus, y=0 is a horizontal asymptote of the graph of f(x).
  • We have that f(x)= 1x→ -∞ as x→ 0^- and f(x)= 1x→ ∞ as x→ 0^+. Thus, x=0 is a vertical asymptote of the graph of f(x).
  • The domain and range of f(x)= 1x are all nonzero real numbers.
  • The graph of f(x)= 1x consists of two parts that are symmetrical with respect to the origin.
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arrow_right Communicate Your Answer p.313
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arrow_right Monitoring Progress p.314-317
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arrow_right Exercises p.318-320
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