SOLUTION: Rational Graphing Can you please help with graphing f(x) = (x^2-6x) / (x-5) Thank you

Question 22813: Rational Graphing
Can you please help with graphing f(x) = (x^2-6x) / (x-5)
Thank you
Answer by eclecticist(12) (Show Source): You can put this solution on YOUR website!
The numerator can be simplified into x(x-6).
This means that there are two zeroes: one at 0 and one at 6.
From the denominator, you can see that there is a vertical asymptote at x-5, because when x = 5, the graph would be undefined.
Also, since the degree of the numerator is 2, and the degree of the degree of the denominator is 1, the degree of the numerator is one greater than the degree of the denominator, resulting in a slant/oblique asymptote. To find this asymptote, you would divide the numerator by the denominator and take the quotient only to find that the slant asymptote is x-1. The shape of the rest of the graph should then be obvious.

RELATED QUESTIONS
Polynomial Graphing, Can you please help with graphing f(x)= 2x^3-x^2-8x+4 Thank... (answered by stanbon!)

Exponential Graphing Can you please help with graphing y = 2(x-1) Thank... (answered by stanbon!)

Having trouble graphing f(x)=2/x-3 Can you please help? (answered by Alan3354)

My son is struggling with these graphing rational functions. Can anyone help? 1. How... (answered by Edwin McCravy,Alan3354)

Please help with graphing the following systems: 4x +5y = -2 4y -x = 11 Thank... (answered by mananth)

f(x)=x^2-36/x+6 I need help graphing this rational function. Thank you so much for (answered by rapaljer)

Graphing function : f(x)= (2x)/(x^2+5x+4) Please help.. I have no idea! THANK... (answered by stanbon)

Can you please graph f(x)= (x^2-6x) / (x-5) Thank you (answered by stanbon)

Hi, I need help graphing this problem f(x)=1/3x-2. Thank... (answered by checkley77)