Sec 2.7: Rational Functions

  1. Find $x$-, $y$-intercepts and holes in the graph of the rational function.   solution

    2. (a) $r(x)=\dfrac{x^2-2x-15}{x-10}$   (b) $r(x)=\dfrac{x^2-9}{x^2}$   (c) $f(x)=\dfrac{3-26 x-9 x^2}{3+16 x+5 x^2}$

  2. Consider each of the following rational functions. Find the domain, hole(s) in the graph and the intercepts.   solution

    3. (a) \( R(x)=\dfrac{4x(x-3)}{(x+8)(x-1)}\)   (b) \( h(x)=\dfrac{x^2-81}{x^2+11x+18}\)

  3. Consider each of the following rational functions. Find the domain, hole(s) in the graph and the intercepts.   solution

    4. (a) \(y = \dfrac{2x^2-3x-5}{-2x^3+5x^2}\)   (b) \( f(x) = \dfrac{14}{x^2+49}\)

  4. Consider the rational function \( R(x)=\dfrac{3x(x-1)}{2x^2-x-1}\). Find the holes in the graph, intercepts, vertical and horizontal asymptotes.    solution

  5. Find any asymptotes and the holes in the graph of the rational function.  solution

    6. (a) $f(x)=\dfrac{x^2+2 x+1}{7 x^2-x-8}$   (b) $f(x)=\dfrac{3-11 x-4 x^2}{3+10 x+3 x^2} $