1. Power Functions and Radical Equations
Lesson 4.7

2. Properties of Exponents
Given
m and m positive integers
r, b and p real numbers

3. Power Function Definition
Where k and p are constants
Power functions are seen when dealing with areas and volumes
Power functions also show up in gravitation (falling bodies)

4. Special Power Functions
Parabola y = x2
Cubic function y = x3
Hyperbola y = x-1

5. Special Power Functions
y = x-2
Text calls them "root" functions

6. Special Power Functions
Most power functions are similar to one of these six
xp with even powers of p are similar to x2
xp with negative odd powers of p are similar to x -1
xp with negative even powers of p are similar to x -2
Which of the functions have symmetry?
What kind of symmetry?

7. Variations for Different Powers of p
For large x, large powers of x dominate x5 x4 x3 x2 x

8. Variations for Different Powers of p
For 0 < x < 1, small powers of x dominate x x4 x5 x2 x3

9. Variations for Different Powers of p
Note asymptotic behavior of y = x -3 is more extreme
0.5 20 10
0.5
y = x -3 approaches x-axis more rapidly
y = x -3 climbs faster near the y-axis

10. Think About It… Given y = x –p for p a positive integer
What is the domain/range of the function?
Does it make a difference if p is odd or even?
What symmetries are exhibited?
What happens when x approaches 0
What happens for large positive/negative values of x?

11. Assignment
Lesson 4.7
Page 321
Exercises 1 – 67 EOO