Rational Functions
1. Consider each of the following rational functions. Find the domain, hole(s) in the graph
and the intercepts. (a) \( R(x)=\dfrac{4x(x-3)}{(x+8)(x-1)}\)
(b) \( h(x)=\dfrac{x^2-81}{x^2+11x+18}\)
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2. Consider each of the following rational functions. Find the domain, hole(s) in the graph
and the intercepts. (a) \(y = \dfrac{2x^2-3x-5}{-2x^3+5x^2}\)
(b) \( f(x) = \dfrac{14}{x^2+49}\)
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3. 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.
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4. Find the horizontal asymptote. Determine if/where the graph of the
function crosses the horizontal asymptote.
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(a) \( y=\dfrac{8x^2+9x-5}{2x^2+1} \)
(b) \( y=\dfrac{3x^2+1}{2x^2+x-7} \)
5. Consider the rational function \(
R(x)=\dfrac{3x^2+1}{4(x-1)(x+3)}\). Find the holes in the graph, vertical
and horizontal asymptotes, and determine if/where the graph crosses the
horizontal asymptote.
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