Transcript power function

Warm-up
Augmented Matrix
Understanding Power Functions
Recognizing the Characteristics of
Power Functions
Power Function
• A power function is a function that can be
represented in the form
• Where the base is a variable and the
exponent, p, is a number.
In your calculator!
• Change the Tblset window on graphing
calculator to TblMin = –10, ΔTbl = 2,
• Set both Indpnt/Depend: Auto. Then graph the
following equations intographing calculator:
• Y1=2X
• Y2=2X^3
• Y3=2X^4
• Y4=2X^2
State the similarities and differences between the functions.
Characteristics of Power Functions
Graph.
f ( x)  x 6
f ( x)  x 4
f ( x)  x 2
What point(s) do the toolkit power functions have in common?
Characteristics of Power Functions
Graph.
With the even power function, as the input
becomes large in either the positive or
negative direction, the output values become
very large positive numbers. Equivalently, we
could describe this by saying that as x
approaches positive or negative infinity, the
f(x) values approach positive infinity.
In symbolic form,
x  
f (x )  
Characteristics of Power Functions
Graph.
f ( x)  x , f ( x)  x , and f ( x)  x
3
5
7
What point(s) do the toolkit power functions have in common?
,
,
Characteristics of Power Functions
Graph.
For these odd power functions, as x
approaches negative infinity,
f(x) approaches negative infinity.
As x approaches positive infinity,
f(x) approaches positive infinity.
In symbolic form
x   f (x)  
x 
f (x )  
Now!
• Graph y=kx^p
• Using different positive integers for (p) and
any real number for (k).
• Then should make notes as to the discoveries
you find.
Pot this function to a graph then identify which
power function fits the data and draw the curve
of the power function.
For any real number x and any positive
integer n, the following are true:
Example
Time for the worksheet 