# I need help Rational function

• Apr 22nd 2008, 12:04 AM
tpwkbs
I need help Rational function
Cosider rational function f(x)= 2x^2 + 7x-5 / x+4

1. Determine if graph has any holes
2. find all asymptopes for f(x)
3. find all intercepts
4. find atleast one point between any verticle asymptope(s) and x-intercepts(s)

Thanks for your help or(Rofl) answers I really need to catch up on studying.
• Apr 22nd 2008, 06:19 AM
mr fantastic
Quote:

Originally Posted by tpwkbs
Cosider rational function f(x)= 2x^2 + 7x-5 / x+4

1. Determine if graph has any holes Mr F says: x + 4 is NOT a factor of 2x^2 + 7x - 5. Therefore no holes.

2. find all asymptopes for f(x) Mr F says: Vertical asymptote should be obvious (hint: when is f(x) undefined). Horizontal asymptote: None. Oblique asymptote: Hint: $\displaystyle {\color{red}f(x) = 2x - 1 - \frac{1}{x + 4}}$.
3. find all intercepts Mr F says: x-intercepts: Hint: Solve 2x^2 + 7x - 5 = 0 (why?). y-intercept: Should be obvious.
4. find atleast one point between any verticle asymptope(s) and x-intercepts(s) Mr F says: Draw the graph. I'd suggest a simple point like one on the x-axis ......

Thanks for your help or(Rofl) answers I really need to catch up on studying. Mr F says: Yes you really do.

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