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Maths-

General

Easy

Question

Graph each function and identify the horizontal and vertical asymptotes
$straight F left parenthesis straight x right parenthesis equals fraction numerator 3 x squared minus 11 x minus 4 over denominator 4 x squared minus 25 end fraction$

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) = p(x)/q(x), where p(x) and q(x) are polynomials such that q(x) ≠ 0.
Rational functions are of the form y = f(x)y = f x , where f(x)f x 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= -5/2 and horizontal asymptote is y = (leading coefficient of numerator) / (leading coefficient of denominator) = 3/4 = 0.75.

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 .
4x² -25 = 0
4x² = 25
x² = $25 over 4$
x = $5 over 2$ and x = $fraction numerator negative 5 over denominator 2 end fraction$
The vertical asymptote of the rational function is x=−1.
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= $fraction numerator negative 5 over denominator 2 end fraction$ and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = $3 over 4$ = 0.75.

Related Questions to study

Graph each function and identify the horizontal and vertical asymptotes
$r left parenthesis x right parenthesis equals fraction numerator 2 x squared plus 7 over denominator 1 plus 2 x plus x end fraction 2$

Graph each function and identify the horizontal and vertical asymptotes
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What is the graph of f(x $table attributes columnspacing 1em end attributes row cell 9 x squared minus 25 end cell row cell x squared minus 5 x minus 6 end cell end table$

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Arrange the following in descending order :
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Order the following from least to greatest :
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