determine whether the following statement is true or false. if the statement is false, make the necessary…
determine whether the following 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 cannot have both a vertical asymptote and a horizontal asymptote. choose the correct answer below. a. the statement is true. b. the statement is false. a true statement is \the graph of a rational function can have both a vertical asymptote and a horizontal asymptote.\ c. the statement is false. a true statement is \the graph of a rational function has several vertical asymptotes and one horizontal asymptote.\ d. the statement is false. a true statement is \the graph of a rational function has at least one vertical asymptote and at least one horizontal asymptotes.\
Answer
Brief Explanations:
A rational function of the form $f(x)=\frac{p(x)}{q(x)}$, where $p(x)$ and $q(x)$ are polynomials, can have vertical asymptotes at the values of $x$ that make $q(x) = 0$ and a horizontal asymptote determined by the degrees of $p(x)$ and $q(x)$. For example, $f(x)=\frac{1}{x}$ has a vertical asymptote at $x = 0$ and a horizontal asymptote at $y=0$. So it is possible for a rational - function to have both.
Answer:
B. The statement is false. A true statement is "The graph of a rational function can have both a vertical asymptote and a horizontal asymptote."