1. Properties of Elementary Functions
Power Functions

2. Power Functions - Algebraically
Parent Function
General Equation:
Translated Function:

3. Power Functions - Graphically
There are two things we talk about with each power graph:
Concavity (Concave Up or Concave Down) and Direction (Increasing or Decreasing)
Concave Down and Increasing
Exponent between 0 and 1
Concave Up and Increasing
Exponent greater than 1
Concave Up and Decreasing
Negative Exponent

4. Power Function – Domain Restrictions
If b>0 then domain is all real numbers
If b<0 then the domain excludes x=0
This is because negative exponents make fractions, and we can’t divide by 0
If b is NOT an integer, the domain excludes negative numbers
For most real world applications of power functions, we restrict the domain to all positive numbers

5. Power Functions – Other Graph Information
If b>0 our graph contains the point (0, 0) (the origin)
If b<0 there are two asymptotes, along the x-axis and y-axis
If b>0 the graph is increasing
If b<0 the graph is decreasing
The graph is concave up if b>1
The graph is concave down if 0<b<1

6. Power Functions - Numerically
Power functions follow a multiplication pattern for both x and y.
To check what type of function a table represents you would usually first check linear and quadratic.
If it isn’t either of those, you would then check power.
Use the y-values that can be multiplied by a constant number to get the next.
Exclude any points that don’t follow this pattern for x
Check the y-values of these points, they should also multiply by a constant.

7. Assignment From Yesterday: From Today:
Pages Problems Q1-Q10 (review of function notation), 11 (parts a&c only), and 13 (parts a&c only)
Pages Problems Q1, Q4, Q9, 5, 8, 11 and 12
For problems 5-8 determine whether each table is linear or quadratic
From Today:
Page 76 Problems 17 (parts a-c) and 18 (parts a-c)
Pages Problems 5, 7 and 10
State whether these three tables represent power functions or not