1. Radical Functions and Rational Exponents
Chapter 6

2. 6.1 Roots and Radical ExpressionsPg
Obj: Learn how to find nth roots.
A.SSE.2

3. 6.1 Roots and Radical Expressions
The nth Root
If aⁿ = b, with a and b real numbers and n a positive integer, then a is an nth root of b.
If n is odd
There is one real nth root of b, denoted in radical form as
If n is even
And b is positive, there are two real nth roots of b. The positive root is the principal root and its symbol is The negative root is its opposite.
And b is negative, there are no real nth roots of b.
The only nth root of 0 is O.

4. 6.1 Roots and Radical Expressions
Index
Radical
Radicand

5. 6.1 Roots and Radical Expressions
nth Roots of nth Powers
For any real numbers a,
a if n is odd
|a| if n is even

6. 6.2 Multiplying and Dividing Radical ExpressionsPg
Obj: Learn how to multiply and divide radical expressions.
A.SSE.2

7. 6.2 Multiplying and Dividing Radical Expressions
Combining Radical Expressions: Products
Simplest Form – a radical that is reduced as much as possible
Combining Radical Expressions: Quotients

8. 6.2 Multiplying and Dividing Radical Expressions
Rationalize the Denominator – rewrite the expression so that there are no radicals in any denominator and no denominator in any radical

9. 6.3 Binomial Radical ExpressionsPg
Obj: Learn how to add and subtract radical expressions.
A.SSE.2

10. 6.3 Binomial Radical Expressions
Like Radicals – radical expressions that have the same index and radicand
Combining Radical Expressions: Sums and Differences

11. 6.4 Rational Exponents Pg. 381 – 388
Obj: Learn how to simplify expressions with rational exponents.
N.RN.2, N.RN.1

12. 6.4 Rational Exponents Rational Exponent
Properties of Rational Exponents

13. 6.5 Solving Square Root and Other Radical EquationsPg
Obj: Learn how to solve square root and other radical equations.
A.REI.2, A.CED.4

14. 6.5 Solving Square Root and Other Radical Equations
Radical Equation – an equation that has a variable in a radicand or a variable with a rational exponent
Square Root Equation – a radical equation that has an index of 2

15. 6.6 Function Operations Pg. 398-404
Obj: Learn how to add, subtract, multiply, and divide functions and to find the composite of two functions.
F.BF.1.b, F.BF.1.c

16. 6.6 Function Operations Function Operations Composition of Functions
(f+g)(x) = f(x) + g(x)
(f-g)(x) = f(x) – g(x)
(f∙g)(x) = f(x) ∙ g(x)
(f/g)(x) = f(x)/g(x), g(x)≠ 0
Composition of Functions
Evaluate f(x) first
Then use f(x) as the input for g

17. 6.7 Inverse Relations and Functions
Pg. 405 – 412
Obj: Learn how to find the inverse of a relation or function.
F.BF.4.a, F.BF.4.c

18. 6.7 Inverse Relations and Functions
If a relation pairs element a of its domain to element b of its range, the inverse relation pairs b with a. If (a,b) is an ordered pair of a relation, then (b,a) is an ordered pair of its inverse.
Inverse Functions – when both the relation and its inverse are functions
One-to-one Function – each y-value in the range corresponds to exactly one x-value in the domain

19. 6.7 Inverse Relations and Functions
Composition of Inverse Functions

20. 6.8 Graphing Radical Functions
Pg. 414 – 420
Obj: Learn how to graph square root and other radical functions.
F.IF.7.b, F.IF.8

21. 6.8 Graphing Radical Functions
Families of Radical Functions
Parent Function
Reflection in x-axis
Stretch (a > 1) or Shrink (0 < a < 1)
Translation: Horizontal by h; Vertical by k