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Maths-

General

Easy

Question

What is the graph of f(x $table attributes columnspacing 1em end attributes row cell 9 x squared minus 25 end cell row cell x squared minus 5 x minus 6 end cell end table$

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 .

The correct answer is: The vertical asymptote of the rational function is x=−1 and x= 6 . This function has the x -intercept at (1.667,0) and y -intercept at (0,1) . We will find more points on the function and graph the function.

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 .
x² - 5x - 6 = 0
x² - 6x + 1x - 6 = 0
x(x - 6) + 1 (x - 6) = 0
(x - 6) (x + 1) = 0
x – 6 = 0 or x + 1 = 0
x = 6 or x = -1
The vertical asymptote of the rational function is x=−1 and x= 6 .
This function has the x -intercept at (1.667,0) and y -intercept at (0,1) . We will find more points on the function and graph the function.

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