Given f(x) = (6x)/(x^2 - 9), find intercepts, asymptotes, limits, intervals of...

Stuck with problem. Can someone please help?

Answer the following questions regarding the function below, and use your answers to sketch the function.

. . . . .\(\displaystyle f(x)\, =\, \dfrac{6x}{x^2\, -\, 9}\)

1. List the x-values of any x-intercepts of f.

2. Give the y-value of the y-intercept of f.

3. List the x-values of any vertical asymptotes of f.

4. Evaluate the following limits:

. . . . .\(\displaystyle \displaystyle \mbox{a. }\, \lim_{x \rightarrow \infty}\, f(x)\)

. . . . .\(\displaystyle \displaystyle \mbox{b. }\, \lim_{x \rightarrow -\infty}\, f(x)\)

5. List the y-values of any horizontal asymptotes of f.

6. Find the intervals on which f is increasing or decreasing.

7. List the coordinates of any local extrema.

8. Find the intervals on which f is concave up or concave down.

9. List the coordinates of any points of inflection.

onty5577 said:

Stuck with problem. Can someone please help?

Answer the following questions regarding the function below, and use your answers to sketch the function.

. . . . .\(\displaystyle f(x)\, =\, \dfrac{6x}{x^2\, -\, 9}\)

1. List the x-values of any x-intercepts of f.

2. Give the y-value of the y-intercept of f.

3. List the x-values of any vertical asymptotes of f.

4. Evaluate the following limits:

. . . . .\(\displaystyle \displaystyle \mbox{a. }\, \lim_{x \rightarrow \infty}\, f(x)\)

. . . . .\(\displaystyle \displaystyle \mbox{b. }\, \lim_{x \rightarrow -\infty}\, f(x)\)

5. List the y-values of any horizontal asymptotes of f.

6. Find the intervals on which f is increasing or decreasing.

7. List the coordinates of any local extrema.

8. Find the intervals on which f is concave up or concave down.

9. List the coordinates of any points of inflection.

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onty5577 said:

Stuck with problem. Can someone please help?

Click to expand...

At which point are you stuck? How are you stuck?

onty5577 said:

Answer the following questions regarding the function below, and use your answers to sketch the function.

. . . . .\(\displaystyle f(x)\, =\, \dfrac{6x}{x^2\, -\, 9}\)

1. List the x-values of any x-intercepts of f.

2. Give the y-value of the y-intercept of f.

Click to expand...

Finding intercepts is just algebra. (here) Where are you getting bogged down in the plugging-zero-in-and-solving process?

onty5577 said:

3. List the x-values of any vertical asymptotes of f.

4. Evaluate the following limits:

. . . . .\(\displaystyle \displaystyle \mbox{a. }\, \lim_{x \rightarrow \infty}\, f(x)\)

. . . . .\(\displaystyle \displaystyle \mbox{b. }\, \lim_{x \rightarrow -\infty}\, f(x)\)

5. List the y-values of any horizontal asymptotes of f.

Click to expand...

Finding asymptotes is from algebra (and the limit stuff above is just the calculus version of the algebra rules). (here) Where are you stuck in the process?

onty5577 said:

6. Find the intervals on which f is increasing or decreasing.

Click to expand...

What did you see when you graphed this in your calculator? What did you determine from the First Derivative Test?

onty5577 said:

7. List the coordinates of any local extrema.

Click to expand...

The extrema are at the zeroes of the first derivative. What did you get?

onty5577 said:

8. Find the intervals on which f is concave up or concave down.

Click to expand...

What did you see when you graphed this in your calculator? What did you determine from the Second Derivative Test?

onty5577 said:

9. List the coordinates of any points of inflection.

Click to expand...

The inflection points are at the zeroes of the second derivative. What did you get?

Please be complete. Thank you!