Kevin R. answered • 01/24/14

K-12/Math/Engineering/Spanish Tutoring

There are two ways to solve this problem. The quickest way is to plot the equation and view the end behaviors.

Since we know that the equation given... f(x) = -2(x-4)^3+11 is to the power of 3. The curve will follow the following pattern:

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\____ or ____/

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After analyzing the graph we can determine the end behavior. If you graph the equation you will find that it follows this pattern:

\

\__(0,0)___

\

\

So as x -> -infinity, y gets bigger and bigger (up), or approaches +infinity

and as x -> +infinity, y goes down or gets bigger and bigger in the negative direction and approaches -infinity

so in all... The steps would be to

1. Determine the power of the function (in english, what number is x raised to).

2. graph the function

3. determine end behavior. (if the line goes up it approaches +infinity, if it goes down it approaches - infinity)

Kevin R.

Yes you are correct. If you go to the website

(http://web.psjaisd.us/auston.cron/ABCronPortal/GeoGebraMenu/Investigating%20Parent%20FunctionsUsing%20GeoGebraGeoGebra%20is%20graphing.htm)

you will see the relationship. All even power functions will look like a parabola and all odd power functions will look like a twisted parabola. (Just note that the higher the power the longer the line will be "flat" in the middle)

As steve mentioned above. The point of inflection is when the second derivative of the function is equal to zero [ f''(x) = 0 ]. A quick way to check is that the point of inflection is usually (not always, but typically) right in the middle of where the graph goes flat.

i.e.

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\_____

^ \

POI \

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01/24/14

Shyanna N.

01/24/14