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Find the value(s) of \(x\) that satisfy
each of the following equations.
\[x=\frac{3x+77}{x}-7\]\[\frac{x^3-2x}{x+2}=\frac{10x}{x+2}-11x\]\[x^2=\frac{6}{x^2+1}\]\[\frac{x(x-3)(x+3)}{16-x}=9\]
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Without the aid of technology, roughly sketch the graph
of the following rational function on the axes below.
Don’t worry too much about the vertical scaling.
\[ a(x) = \frac{(x+5)(x-8)}{x-3} \]
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Without the aid of technology, roughly sketch the graph
of the following rational function on the axes below.
Don’t worry too much about the vertical scaling.
\[ b(x) = \frac{(x+5)^2(x-8)^3}{(x-3)^4} \]
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Without the aid of technology, roughly sketch the graph
of the following rational function on the axes below.
Don’t worry too much about the vertical scaling.
\[ c(x) = \frac{(x+2)(x+5)(x+10)}{x(x+7)} \]
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Without the aid of technology, roughly sketch the graph
of the following rational function on the axes below.
Don’t worry too much about the vertical scaling.
\[ d(x) = \frac{(x+2)(x+5)^2(x+10)^4}{x^6(x+7)^2} \]
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Without the aid of technology, roughly sketch the graph
of the following rational function on the axes below.
Don’t worry too much about the vertical scaling.
\[ f(x) = \frac{x}{(x-9)(x+3)(x+9)} \]
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Without the aid of technology, roughly sketch the graph
of the following rational function on the axes below.
Don’t worry too much about the vertical scaling.
\[ g(x) = \frac{x^2}{(x-9)^2(x+3)^3(x+9)} \]