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Chapter 3: Problem 1
Find the domain of each rational function. $$f(x)=\frac{5 x}{x-4}$$
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Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. No quadratic functions have a range of \((-\infty, \infty)\)
If you are given the equation of a rational function, how can you tell if the graph has a slant asymptote? If it does, how do you find its equation?
The equation for \(f\) is given by the simplified expression that results after performing the indicated operation. Write the equation for \(f\) and then graph the function. $$\frac{x}{2 x+6}-\frac{9}{x^{2}-9}$$
If you are given the equation of a rational function, explain how to find the horizontal asymptote, if any, of the function's graph.
Use everyday language to describe the behavior of a graph near its vertical asymptote if \(f(x) \rightarrow \infty\) as \(x \rightarrow-2^{-}\) and \(f(x) \rightarrow-\infty\) as \(x \rightarrow-2^{+}\)
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