How do you graph x^4?

[Chemistry101]

How do you graph x^4?
I understand that x^2 is over 1 up 1 over 1 up 3 over 1 up 5 etc...

But for x^4? What is it? When I plugged it into the calculator the graphs were totally different?

Help?

 

[jacksonpeeble]

I'm not entirely sure that I understand what you're asking.

If your function is f(x)=x^4, that simply means that for every x value, you must take the fourth power of that. For example, f(1)=1^4=1*1*1*1=1, and f(2)=2^4=2*2*2*2=16. Your graph should look very similar to x^2 and should be in a parabola form that opens upwards and has a vertex of (0,0). The only difference is the x^4 will increase much more rapidly; however, the general shape will hold. Try changing your window to something narrower but taller. Also, make sure that your calculator is in the correct mode (avoid radians in this case).

Did this answer your question, or did I misunderstand?

 

[Borek]

How do you graph x^4?
I understand that x^2 is over 1 up 1 over 1 up 3 over 1 up 5 etc...

(x+1)² - x² = x² + 2x + 1 - x² = 2x + 1

But for x^4?

Won't be that easy, the difference grows with 3rd power of x (plus some other terms).

 

[HallsofIvy]

How do you graph x^4?
I understand that x^2 is over 1 up 1 over 1 up 3 over 1 up 5 etc...

Yes, because 0²= 0, 1²= 1, and 1- 0= 1. 2²= 4, and 4- 1= 3. 3²= 9, and 9- 4= 5, etc.
0⁴= 0, 1⁴= 1, and 1- 0= 1. 2⁴= 16 and 16-1= 15. 3⁴= 81, and 81- 16= 65: You go "over 1 up 1, over 1 up 15, over 1 up 65, etc. (Assuming, of course, that you are starting at (0,0).)

You understand, I hope, that it is the value of the function that is important. Going "over 1 up ..." is one particular (and slightly unusual) shortcut.