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Chapter 3: Problem 43
Find the horizontal asymptote, if there is one, of the graph of each rational function. $$ f(x)=\frac{-2 x+1}{3 x+5} $$
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Use a graphing utility to graph \(f\) and \(g\) in the same viewing rectangle. Then use the ZOOM OUT feature to show that f and g have identical end behavior. \(f(x)=-x^{4}+2 x^{3}-6 x, \quad g(x)=-x^{4}\)
Determine whether each statement is true or false If the statement is false, make the necessary change(s) to produce a true statement. It is possible to have a rational function whose graph has no \(y\) -intercept.
Crosses the \(x\)-axis at \(-4,0,\) and \(3 ;\) lies above the \(x\)-axis between \(-4\) and \(0 ;\) lies below the \(x\)-axis between 0 and 3
In Exercises 100鈥�103, determine whether each statement makes sense or does not make sense, and explain your reasoning. Although I have not yet learned techniques for finding the \(x\) -intercepts of \(f(x)=x^{3}+2 x^{2}-5 x-6,\) I can easily determine the \(y\) -intercept.
Determine whether each statement is true or false If the statement is false, make the necessary change(s) to produce a true statement. The graph of a rational function can have three vertical asymptotes.
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