Radical Functions and Rational Exponents Chapter 6

6.1 Roots and Radical Expressions Pg. 361-366 Obj: Learn how to find nth roots. A.SSE.2

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.

6.1 Roots and Radical Expressions Index Radical Radicand

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

6.2 Multiplying and Dividing Radical Expressions Pg. 367-373 Obj: Learn how to multiply and divide radical expressions. A.SSE.2

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

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

6.3 Binomial Radical Expressions Pg. 374-380 Obj: Learn how to add and subtract radical expressions. A.SSE.2

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

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

6.4 Rational Exponents Rational Exponent Properties of Rational Exponents

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

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

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

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

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

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

6.7 Inverse Relations and Functions Composition of Inverse Functions

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

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