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Math Help - I need help Rational function

  1. #1
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    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 answers I really need to catch up on studying.
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  2. #2
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    Quote Originally Posted by tpwkbs View Post
    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: {\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 answers I really need to catch up on studying. Mr F says: Yes you really do.
    ..
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