Formulas, graphs & relations » Power relation

Contents

1. General
2. Formula
3. Graph

1. General

A power relation(ship) corresponds to a formula with a power in it. You can use these formulas for lines that increase very fast. For example, the height of a rocket that is being launched or the time it takes to crack a password.

2. Formula

The formula is always of the type y = a · xn.
Examples are h = –10 · x8 en a = 3b5.
The formula y = 7x2 is a quadratic formula and a power formula.
With h = –10x4 + 3x3 – 5x2 + 2x + 3 you have a polynomial in stead of a power formula. In this case a polynomial to the fourth degree.

Note:
When substituting x for a negative number in a power, you will get brackets around the negative number!

Example

Given is the following formula y = 7x4.
Calculate y when x = –3.
Answer: y = 7(–3)4 = 7 · 81 = 567

3. Graph

The graphs corresponding to power relations have different shapes.
The shape depends on a positive or negative number in front of x and on an odd or even exponent in the formula.

y = pxeven
graph y = px^even
y = pxodd
graph y = px^odd
   
y = nxeven
graph y = nx^even
y = nxodd
graph y = nx^odd


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