# Math Assignment Help With Horizontal Asymptotes

## 4.5.2 Horizontal Asymptotes

*f*(*x*) = 2*x* – 1

*x*

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

x | 1 | 10 | 102 | 103 |

f(x) | 1 | 1.9 | 1.99 | 1.999 |

- 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 2*x* and the denominator has only one term *x*. Therefore *f*(*x*) takes values closer to 2*x* / *x* = 2. See graphical behaviour below.

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