Sketching a graph help

nickp657

New member
Joined
Aug 10, 2010
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1
Hi guys I have this set of parameters

Domain is (-00,00)
The only intercept x-intercept is x=0
Lim x->00 f(x)=-00 lim x->-00 f(x)=0
f(x) is negative for x>0 and f(x) is positive for x<0 Moreover f(1)=-9 and f(-2)=2 and f(-1)=3
f'(x) is 0 only at x = -1 Moreover, f'(-4) positive while f'(4) is negative
f''(x) is 0 only at x=-2 Moreover, f''(-6) is positive while f''(4) is negative

Now I know how the graph goes but once I hit (1,-9) I am confused, also the other problem is I can't tell if this graph has any asymptoes or local mins. Any help would be great thanks.
 
nickp657 said:
Domain [of function f] is (-00,00)

Lim x->00 f(x)=-00 lim x->-00 f(x)=0

f`(x) is 0 only at x = -1

:idea: These three lines provide key information about asymptotes and extrema :idea:



I can't tell if this graph has any asymptotes or local mins Here are some questions for you to consider.

Regarding local minimums or maximums [extrema], do you know what it means graphically when a function's first derivative equals zero ?

Regarding horizontal asymptotes, if there were any, what would they do to the function's global behavior ?

Regarding vertical asymptotes, if there were any, what would they do to the domain of the function ?



I know how the graph goes ? I do not know what this statement means.



once I hit (1,-9) I am confused Can you be more specific ?

 
Hello, nickp657!

There is a lot of information in thse statements. . .


Given a function f(x):\displaystyle \text{Given a function }f(x):

\(\displaystyle \text{Domain is: }\:(-\infty,\:\infty)\)
The graph exists for all values of x.

The only x-intercept is: x=0\displaystyle \text{The only }x\text{-intercept is: }\:x = 0
The graph crosses the x-axis only at the Origin.

limxf(x)=\displaystyle \lim_{x\to\infty} f(x) \:=\:-\infty
To the far right, the graph falls lower and lower . . .
limx-=0\displaystyle \lim_{x\to\text{-}\infty} \:=\:0
To the far left, the graph approaches the x-axis.

f(x)<0 for x>0\displaystyle f(x) < 0 \text{ for }x>0
On the right, the graph is below the x-axis.
f(x)>0 for x<0\displaystyle f(x) > 0 \text{ for }x<0
On the left, the graph is above the x-axis.
f(1)=-9,  f(-2)=2,  f(-1)=3\displaystyle f(1 )=\text{-}9,\;f(\text{-}2)=2,\; f(\text{-}1)=3
We are given three points on the graph.

f(x)=0 only at x=-1\displaystyle f'(x) = 0\,\text{ only at }\,x = \text{-}1
The only horizontal tangent is at (-1,3).
f(-4)>0\displaystyle f'(\text{-}4) > 0
At x = -4, the graph is increasing.
f(4)<0\displaystyle f'(4) < 0
At x = 4, the graph is decreasing.

f(x)=0 only at x=-2\displaystyle f''(x) = 0\,\text{ only at }\,x=\text{-}2
The only inflection point is (-2,2).
f(-6)>0\displaystyle f''(\text{-}6) > 0
At x = -6, the graph is concave up.
f(4)<0\displaystyle f''(4) < 0
At x = 4, the graph is concave down.

I believe the graph looks like this . . .
Code:
                   (-1,3)             |
                      o               |
         (-2,2) *           *         |
             o                  *     |
          *                        *  |
     *                               *|
  - - - - - - - - - - - - - - - - - - o - - - - -
                                      |*
                                      |
                                      | * 
                                      |
                                      |
                                      | -*





*
[/size]
 
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