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Maths-

General

Easy

Question

Identify the asymptotes and sketch the graph of $straight g left parenthesis straight x right parenthesis equals fraction numerator straight x squared minus 5 straight x plus 6 over denominator 2 straight x squared minus 10 end fraction$

hint 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) = $fraction numerator straight p left parenthesis straight x right parenthesis over denominator straight q left parenthesis straight x right parenthesis end fraction$ , 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 .
2x² - 10 = 0
2x² = 10
x² = 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) = $1 half$ =0.5

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