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 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, y = 8. (type an equation.) c. the function has no horizontal asymptotes. determine the slant asymptote(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the slant asymptote(s) is(are) (type an equation. use a comma to separate answers as needed.) b. the function has no slant 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 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, y = 8. (type an equation.) c. the function has no horizontal asymptotes. determine the slant asymptote(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the slant asymptote(s) is(are) (type an equation. use a comma to separate answers as needed.) b. the function has no slant asymptotes.

Answer

Explanation:

Step1: Rewrite the function

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

Step2: Find horizontal asymptote

As $x\to\pm\infty$, $\lim_{x\to\pm\infty}(8 - \frac{3}{x})=8$. So the horizontal - asymptote is $y = 8$.

Step3: Determine slant asymptote

Since the degree of the numerator is equal to the degree of the denominator, there is no slant asymptote. A slant asymptote occurs when the degree of the numerator is one more than the degree of the denominator.

Answer:

For the horizontal asymptote: B. The function has one horizontal asymptote, $y = 8$. For the slant asymptote: B. The function has no slant asymptotes.