Maths-

General

Easy

Question

# How do you find vertical and horizontal asymptotes of a rational function?

What are the vertical asymptotes for the graph of

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: From the graph we can analyze that the vertical asymptote of the rational function is x = -3 and x = -4.

- Find the asymptotes of the rational function, if any.
- Draw the asymptotes as dotted lines.
- Find the x -intercept (s) and y -intercept of the rational function, if any.
- Find the values of y for several different values of x .
- 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 .

x^{2} +7x + 12 = 0

x^{2} + 3x + 4x + 12 = 0

x(x + 3) + 4 (x + 3) = 0

(x + 3)(x + 4)=0

x= -3 or x = -4

The vertical asymptote of the rational function is x=−3 and x=-4

This function has no x -intercept at (4,0) and y -intercept at (0,7) . We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is x= -3 and x = -4.

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