Graphing a Rational Function

Question

Please help me graph this rational function g(x) = (-5x)/(x²-9)

I'm stuck with plotting the points and sketching the graph.

Answer 1

You need to know how to calculate limits from the left and from the right.

 

Consider the values of x that make the denominator (x²-9)=0 which will give you the locations of the vertical asymptotes. You have to calculate the limits from the left and from the right at the asymptotes. There are two vertical asymptotes in this case.

 

To get the horizontal asymptotes you calculate limits of g(x) when x goes to ± infinity. There is one horizontal asymptote in this case.

 

You also need to find the value of x for which g(x)=0. A hint for this case: find the value of x for which the numerator is zero.

 

I hope it helps you.