sketching the graph of (x^3-3x+2)/(x^2-9) without the use of a calculator

[mitch_996]

The question is to graph the function (x^3-3x+2)/(x^2-9) without the use of a calculator. The question also states that there is no need to consider the second deriviative.

I've tried using the quotient rule to find the turning points but i end up with a 4th order equation on the top and bottom of the fraction which makes it very hard to find the roots of.

 

[Deleted member 4993]

The question is to graph the function (x^3-3x+2)/(x^2-9) without the use of a calculator. The question also states that there is no need to consider the second deriviative.

I've tried using the quotient rule to find the turning points but i end up with a 4th order equation on the top and bottom of the fraction which makes it very hard to find the roots of.

Couple of things I would consider for plotting:

1. Can I factorize the numerator and the denominators? What does that tell me about the nature of the function?
2. Are there vertical and/or horizontal asymptotes? What does that tell me about the nature of the function?

Then I would start thinking about turning point and such .......

 

[crybloodwing]

The question is to graph the function (x^3-3x+2)/(x^2-9) without the use of a calculator. The question also states that there is no need to consider the second deriviative.

I've tried using the quotient rule to find the turning points but i end up with a 4th order equation on the top and bottom of the fraction which makes it very hard to find the roots of.

1. First I would see if I could simplify the function in some form. For a quadratic, using factoring may be the best way.

For the bottom, remember the rule that if you have (a+b)(a-b) you will get (a²-b²).

The denominator(bottom) will help you determine values that can not exists. AKA, values for x that make the bottom 0. These will be vertical asymptotes so draw a dotted line on the graph at these x values.

2. Create a table of values excluding the ones that make the bottom 0. Plug these values in and create a list of points.

3. Draw the graph from these points.

4. As you near a vertical asymptote, find the y values for close points. For example, if the VA is 2, find points at 1, 1.5, 2.5, and 3. This can show you how the graph moves when it reaches the VA.