Math Assignment Help With Horizontal Asymptotes

4.5.2 Horizontal Asymptotes

f(x) = 2x – 1

x

  1. i) Let’s find the value of f(x) for increasing values of x.
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x

1

10 102 103
f(x) 1 1.9 1.99 1.999
  1. ii) Let’s find the value of f(x) for decreasing values of x
x -1 -10 -102 -103
f(x) 3 2.1 2.01 2.001

As | x | increases, the numerator is dominated by the term 2x and the denominator has only one term x. Therefore f(x) takes values closer to 2x / x = 2. See graphical behaviour below.

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