sketch the graph of the following function. indicate where the function is increasing or decreasing, where…

sketch the graph of the following function. indicate where the function is increasing or decreasing, where any relative extrema occur, where asymptotes occur, where the graph is concave up or concave down, where any points of inflection occur, and where any intercepts occur. f(x) = (8x - 3)/x (type equations.) b. the function has one vertical asymptote, x = 0. (type an equation.) c. the function has no vertical asymptotes. determine the horizontal asymptote(s). select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. a. the function has two horizontal asymptotes. the top asymptote is and the bottom asymptote is (type equations.) b. the function has one horizontal asymptote, (type an equation.) c. the function has no horizontal asymptotes.

sketch the graph of the following function. indicate where the function is increasing or decreasing, where any relative extrema occur, where asymptotes occur, where the graph is concave up or concave down, where any points of inflection occur, and where any intercepts occur. f(x) = (8x - 3)/x (type equations.) b. the function has one vertical asymptote, x = 0. (type an equation.) c. the function has no vertical asymptotes. determine the horizontal asymptote(s). select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. a. the function has two horizontal asymptotes. the top asymptote is and the bottom asymptote is (type equations.) b. the function has one horizontal asymptote, (type an equation.) c. the function has no horizontal asymptotes.

Answer

Explanation:

Step1: Rewrite the function

$f(x)=\frac{8x - 3}{x}=8-\frac{3}{x}$

Step2: Find vertical asymptote

The function is undefined when $x = 0$. As $x\to0^{+}$, $f(x)\to+\infty$ and as $x\to0^{-}$, $f(x)\to-\infty$. So the vertical - asymptote is $x = 0$.

Step3: Find horizontal asymptote

We find the limit as $x\to\pm\infty$. $\lim_{x\to\pm\infty}(8-\frac{3}{x})=8$. So the horizontal asymptote is $y = 8$.

Answer:

For vertical asymptote: B. The function has one vertical asymptote, $x = 0$. For horizontal asymptote: B. The function has one horizontal asymptote, $y = 8$.