An example of an integer power function is:
Where x can be any variable and n is a whole number either positive or negative
This is where n would be equal to any positive whole number
Some examples of this are:
The basic shape of x to the power of an even number is a U shape, this we can see in the blue and black graphs above.
The basic shape of x to the power of an odd number is close to an S shape, this we can see in the red graph above.
For the non-transformed positive integer power functions we have a few rules:
When multiple power functions are added together they become polynomials and we will describe sketching them in the quadratic, polynomial and cubic sections.
The second type of a power function is an inverse function where we have x to the power of any negative integer or one over x to the power of any positive integer.
Where n would be equal to any positive whole number
Let’s look at an even and odd example of this:
For the non-transformed negative integer power functions we have a few rules, which are the same as the positive integer power function:
Then we have one rule which is the opposite of the positive integer power function:
We also have a few different rules
Note: means approaching zero from the positive side and from the negative side
Once these basic rules have been mastered transformations can be applied later on to graph more complex functions.
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