Radical Functions and Rational Exponents

1. Radical Functions and Rational Exponents Chapter 6

2. 6.1 Roots and Radical Expressions • Pg. 361-366 • 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 Expressions • Pg. 367-373 • 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 Expressions • Pg. 374-380 • 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 Equations • Pg. 390-397 • 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 • (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 • Inverse Relation • 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