Question

Which graph represents the rational function f(x)=x^2-16/x^2-2x-8?

Answer 1

Answer:

I have provided a graph for the function in the attached file. Hope this helps!

:)

Step-by-step explanation:

Answer 2

Answer:

Check this out below

Step-by-step explanation:We have here a Rational function graph. y=$y=\frac{P(x)}{Q(x)}$ Since on the numerator we have a quadratic function x²-16 and on the denominator x²-2x-8.

Even though we have quadratic functions both on the numerator and on denominator the graph of this Rational Function has another curve, not a parabola

To graph a Rational Function like this we have to :

1) Calculate the x-intercepts from the function on the numerator, mark the points. Find the y-intercepts

x²-16=0

x=+4 and x=-4

x-intercepts

Mark.

Search for any symmetry

2) Calculate the zeros for the Function on the Denominator (in this case x²-2x-8) and mark each vertical asymptote

x²-2x-8=0

x=4 and x=-2 as the vertical asymptotes

3) Find horizontal or inclined asymptotes

4) Make a Study of all Signs, if necessary so that you can check the behavior of the curve close to the asymptotes

5) Make a table pick values for x and then plug it in to get the values for y.

6) Trace the curve.