Exponents and their effects on lines?

[galatians]

Why is it that in a formula: f(x)=2x^4...), why is it that the exponent actually BENDS the line that the fomula makes when it is graphed? I know about the high and low point in algebra two (that's what I'm taking), but i just want to know WHY does an exponent BEND the line?

CD

 

[whatta]

because x^4 grows faster at x2 than at x1, if x2 > x1.

in contrast, x^1 grows at same rate everywhere. you might try to read this without waiting for them to teach you that, if you really need to know.

 

[uart]

Why is it that in a formula: f(x)=2x^4...), why is it that the exponent actually BENDS the line that the fomula makes when it is graphed? I know about the high and low point in algebra two (that's what I'm taking), but i just want to know WHY does an exponent BEND the line?

CD

Your question is a bit like asking : "Why is 2 times 2 more than twice as large as 1 times 1.

 

[symbolipoint]

Please do not confuse a line with a curve. An equation of two variables, both to the first power, represents a line. If either or both variables are raised to other powers than 1, then this represents a curve.

 

[Werg22]

A line is only the special case where a polynomial is of degree 1, which is of the form mx + b Any exponent different than 1 will not give a straight line as the rate of change cannot possibly be constant (the geometrical and analytical definition of a straight line). For instance, for the equation y = x, you have

x y
1 1
2 2
3 3

Here, the difference in y between two consecutive x is always constant, it's equal to 1. For y = x^2 we have,

x y
1 1
2 4
3 9

Here, 9 - 4 is not equal to 4 -1, so the rate of change is dependant on the interval on which you evaluate it.

 

[galatians]

Ohhh...okay. so, like the slope formula, y=mx+b, if the x is squared or has a greater degree than 1, then it's like the 'rise and run' of the thing becomes different, Like, as you showed, instead of it being a rise (y) of 1, 2,3 and a run (x) or 1,2,3; it is now a rise (y) or 1,4,9 and a run (x) of 1,2,3. If it's graphed, then the line actually begins to curve, because its rise and run are no longer constant 1,2,3. is that right? i think it is..

 

[Werg22]

Yes it is.