Polynomial function transformation help

AI Thread Summary
The discussion focuses on understanding the differences between the polynomial functions f(x) = x^3 and g(x) = x^3 - x, specifically how the -x affects the graph. The -x term introduces a linear component that alters the shape and position of the graph, making it appear more linear in certain ranges. Participants suggest evaluating specific points to visualize the transformations and differences between the functions. The conversation emphasizes the importance of graphing to comprehend these transformations effectively. Overall, the transformation impacts the graph's behavior and shape significantly.
Nelo
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Homework Statement


What is the difference between f(x)= x^3 , and g(x) = x^3 - x

What does that -x do to the function and how do you represent it graphically?

What about f(x) = 3x^3 +x


Homework Equations





The Attempt at a Solution



No idea, wolframalphad the graph but i don't get how to represent it or what it does to the graph.

Anyone help please??
 
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any1..?
 
Nelo said:

Homework Statement


What is the difference between f(x)= x^3 , and g(x) = x^3 - x

There's a lot of differences. Are you just supposed to list all of the differences that you can find?

Nelo said:
What does that -x do to the function and how do you represent it graphically?

This is also not worded very well. What does it do to f(x) how? As far as graphing it goes, just pick a few points and plug them in.
 
Yes.. list the differences, I don't get it.
 
So...

x^3 has points

-2 -8
-1 -1
0 0
1 1
2 8


So doing x^3 + x would be

-2 (-2)^3 + -2 = -10
-1 -2
0 0
1 2
2 10

I graphed it... looks almost exactly like a linear function, passes thru vertex to.. is taht right then?
 
zzz, anyone?
 

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