Maths-

General

Easy

Question

# Identify the asymptotes and sketch 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 .

## The correct answer is: The vertical asymptote of the rational function is x = 2.24 and x = -2.24 . horizontal asymptote is y = (leading coefficient of numerator) / (leading coefficient of denominator) = 1/2=0.5

- 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 .

2x^{2} - 10 = 0

2x^{2} = 10

x^{2} = 5

x = 2.24 or x = -2.24

The vertical asymptote of the rational function is x= 2.24 and x= -2.24 .

We will find more points on the function and graph the function.

horizontal asymptote is

y = (leading coefficient of numerator) / (leading coefficient of denominator) ==0.5

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