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Easy

Question

# Use long division to rewrite each rational function, What are the asymptotes of f ? Sketch the graph.

Hint:

### A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational function if, it can be represented as f(x) =, where p(x) and q(x) are polynomials such that q(x) ≠ 0.

Rational functions are of the form y = f(x)y = fx , where f(x)fx is a rational expression .

- If both the polynomials have the same degree, divide the coefficients of the leading terms. This is your asymptote.
- If the degree of the numerator is less than the denominator, then the asymptote is located at y = 0 (which is the x-axis).
- If the degree of the numerator is greater than the denominator, then there is no horizontal asymptote.

## The correct answer is: As square cannot be negative the given function has no asymptote

### 1.Find the asymptotes of the rational function, if any.

2.Draw the asymptotes as dotted lines.

3.Find the x -intercept (s) and y -intercept of the rational function, if any.

4.Find the values of y for several different values of x .

5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.

The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .

1 + 3x^{2 }= 0

x^{2} =

As square cannot be negative the given function has no asymptote

^{2 }= 0

x

^{2}=

As square cannot be negative the given function has no asymptote

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