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Wie zeichnet man eine Potenzfunktion (wie z.B. "f(x) = (x-7)⁷+2") ein?

 25.01.2017
 #1
avatar+1113 
0

Hallo, 

 

wie jede andere Funktion auch. Du wählst dir beliebige x Werte, und rechnest die dazugehörigen y- Werte aus. Und dann trägst du diese in dein Koordinatensystem ein. 

 

\(f(x)=y=(x-7)^7+2\)

 

 

am besten eignet sich einen Wertetabelle dafür.
 

Wertetabelle
x y
-1 -2097150
0 -823541
1 -279934
2 -78123
3 -16382
4 -2185
5 -126
6 1
7 2
8 3
...  

 

 

gruß

 25.01.2017
 #2
avatar+103689 
0

How to Draw a a power function (such as "f (x) = (x-7) ⁷ + 2")?

 

f (x) = (x-7) ⁷ + 2

 

This is a polynomial with a y intercept at 

 -7^7+2 = -823,541

 

It has only one real root at -2^(1/7)+7 = -2^(1/7)+7 = 5.8959104863261877

So its root is at approx x=5.9

 

One end of the polynomial is in the top right hand corner.  Since the leading coefficient is 1 which is positive

and

Since the degree (7) is an odd number the other end of the polynomial will be in the bottom left hand corner.

 

There will be one long almost horizontal line with (7,2) in the middle of it but other than that the curve will be very steep.  It will look a little like a translated y=x^3

 

I predict all this without the use of any calculus.  Of course if you use calculus you can get more precise information. :)

 

Lets see if I have predicted it correctly :)

The red graph is y=x^3

The blue graph is  y=(x-7)^7+2

 

YES it is exactly as I predicted :)

 

 

https://www.desmos.com/calculator/xb15fx16kc

 

 26.01.2017

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