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Maths-

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Easy

Question

What is the graph of $f left parenthesis x right parenthesis equals fraction numerator 4 x squared minus 9 over denominator x squared plus 2 x minus 15 end fraction$

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= 3 and x= -5 . 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 + 2x - 15= 0
x² + 5x -3x - 15= 0
x(x + 5) - 3 (x + 5) = 0
(x – 3) (x + 5) = 0
x – 3 = 0 or x + 5 = 0
x = 3 or x = -5
The vertical asymptote of the rational function is x = 3 and x = -5 .
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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