# Math Help - Rational Function Graph

1. ## Rational Function Graph

Hey Guyzzz,
I need help with a rational function question, I am given a graph with the following things on it:

1) Vertical Asymptote: x = 1
2) Horizontal Asymptote: y = 1 (The graph doesn cross this asymptote on the +ve. x- and y- axis SIDE)
3) Y-Intercept: -4
4) X-INtercept: -2 and 2
5) Point Discontinuity: x = -5 and x = 8

The Question is Determine a possible equation for this graph.
I have even also attached the Graph that will help you guyz.

Thank you.

2. Originally Posted by MordernWar2
Hey Guyzzz,
I need help with a rational function question, I am given a graph with the following things on it:

1) Vertical Asymptote: x = 1

the factor (x-1) in the denominator

2) Horizontal Asymptote: y = 1 (The graph doesn cross this asymptote on the +ve. x- and y- axis SIDE)

degree of numerator = degree of denominator and the ratio of leading coefficients = 1

3) Y-Intercept: -4

f(0) = -4

4) X-INtercept: -2 and 2

(x+2)(x-2) factors in the numerator

5) Point Discontinuity: x = -5 and x = 8

factors (x+5)(x-8) in both the numerator and denominator

The Question is Determine a possible equation for this graph.
I have even also attached the Graph that will help you guyz.

Thank you.

put it all together

3. ## Hey Skeeter

Hey Skeeter, I have put all othe them together, and here have a look at it.

$(x+2)(x-2)(x+5)(x-8) / (x-1)(x+5)(x-8)$

$(x^2 -4)(x^2 - 3x - 40) / (x-1)(x^2 - 3x - 40)$

$(x^4 - 3x^3 - 40x^2 - 4x^2 +12x + 160) / (x^3 - 3x^2 - 40x - x^2 + 3x + 40)$

$(x^4 - 3x^3 - 44x^2 +12x + 160) / (x^3 - 4x^2 - 37x + 40)$

And this is a totally different graph; it has an Oblique (Diagonal Asymptote) because the degree of the numerator is greater than (by 1) the degree of the denominator.

So can you please tell how i would do this question?

4. $f(x)=\frac{(x+2)(x-2)(x+5)(x-8)}{(x-1)^2(x+5)(x-8)}$

You didn't match numerator and denominator degrees.

5. ## Thank You Very Much!!

Hey Guyzzz,
Thank you very much for helping m out here.
I really appreciate it!!...

Special thanks to Skeeter, and Mr. Fantastic for helping with both of my threads.