# Math Assignment Help With Analysis And Graphing Of Rational Functions

## 4.5 Analysis and graphing of Rational Functions:

Let us understand this part of rational functions using an example as given below:

Analyze and graph the rational function whose rule is

*f* (*x*) = 2*x* - 3

* x* – 4

### Vertical Asymptotes

Let,

*f*(*x*) = 2

*x* - 4

The domain of ** f ** is the set of all real numbers except 4, since 4 makes the denominator zero and the division by zero is not defined in mathematics. Let us calculate function

**at values of**

*f**x*close to 4 such that

*x*< 4.

| 0 | 2 | 3 | 3.5 |

f(x) | -0.5 | -1 | -2 | -4 |

Let us now evaluate ** f** at values of

*x*close to 4 such that

*x*> 4

x | 6 | 5 | 4.5 | 4.6 |

f(x) | 1 | 2 | 4 | 0.33 |

- i) As
*x*approaches 4 from the left or by values smaller than 4,*f*(*x*) decreases without bound. - ii) As
*x*approaches 4 from the right or by values larger than 4,*f*(*x*) increases without bound.

We say that the line *x* = 3, broken line, is the vertical asymptote for the graph of ** f**.

In general, the line *x* = a is a vertical asymptote for the graph of ** f ** if

*f*(

*x*) either increases or decreases without bound as

*x*approaches a from the right or from the left. This is symbolically written as:

*f*(*x*) → ∞ *f*(*x*) → -∞

as *x →* a+ or *x →* a-

### Email Based Assignment Help in Analysis And Graphing Of Rational Functions

**To submit Analysis And Graphing Of Rational Functions assignment click here.**