6 Chapter Review

Connecting BIG ideas and Answering the Essential Questions

1 Equivalence You can simplify the nth root of an expression that contains an nth power as a factor. x n n = x n n = x , n  odd | x | , n  even table with 1 row and 2 columns , row1 column 1 , the th , root of x to the n end root , , equals , x super n over n end super , equals , column 2 table with 2 rows and 1 column , row1 column 1 , x comma n , odd , row2 column 1 , absolute value of x , , comma n , even , end table , end table	Radical Expressions and Rational Exponents (Lessons 6-1, 6-2 and 6-4) − 8 x 5 3 x 2 3 = − 8 x 7 3   = ( − 2 ) 3 x 6 ⋅ x 3   = − 2 x 2 x 3 ( − 8 x 5 ) 1 3 ( x 2 ) 1 3 = ( − 8 x 7 ) 1 3   = ( ( − 2 ) 3 ⋅ x 6 ⋅ x ) 1 3   = − 2 x 2 x 1 3 table with 6 rows and 2 columns , row1 column 1 , cube root of negative 8 , x to the fifth end root , . cube root of x squared end root , , column 2 equals . cube root of negative 8 , x to the seventh end root , , row2 column 1 , , column 2 equals . cube root of open , negative 2 , close cubed . x to the sixth , dot x end root , , row3 column 1 , , column 2 equals negative 2 , x squared , cube root of x , , row4 column 1 , open . negative 8 , x to the fifth . close super 1 third end super . open , x squared , close super 1 third end super , column 2 equals . open . negative 8 , x to the seventh . close super 1 third end super , row5 column 1 , , column 2 equals . open . open , negative 2 , close cubed . dot , x to the sixth , dot x . close super 1 third end super , row6 column 1 , , column 2 equals negative 2 , x squared . x super 1 third end super , end table	Solving Square Root Equations (Lesson 6-5) x − 2 = x x 2 − 4 x + 4 = x x 2 − 5 x + 4 = 0 ( x − 4 ) ( x − 1 ) = 0 x = 4  or  x = 1 4 − 2 = 4 ✓ 1 − 2 ≠ 1 ✗ table with 2 rows and 1 column , row1 column 1 , table with 5 rows and 2 columns , row1 column 1 , x minus 2 , column 2 equals square root of x , row2 column 1 , x squared , minus 4 x plus 4 , column 2 equals x , row3 column 1 , x squared , minus 5 x plus 4 , column 2 equals 0 , row4 column 1 , open , x minus 4 , close . open , x minus 1 , close , column 2 equals 0 , row5 column 1 , x equals 4 . or . x equals 1 , end table , row2 column 1 , table with 2 rows and 2 columns , row1 column 1 , 4 minus 2 , column 2 equals square root of 4 check mark , row2 column 1 , 1 minus 2 , column 2 not equal to square root of 1 ballot x , end table , end table
2 Solving Equations and Inequalities When you square each side of an equation, the resulting equation may have more solutions than the original equation. 3 Function If f and f − 1 f super negative 1 end super  are inverse functions and if one maps a to b, then the other maps b to a, i.e., ( f ∘ f − 1 ) ( a ) = ( f − 1 ∘ f ) ( a )   = a . table with 2 rows and 3 columns , row1 column 1 , open f composition , f super negative 1 end super , close open eh close , column 2 equals , column 3 open , f super negative 1 end super , composition f close open eh close , row2 column 1 , , column 2 equals , column 3 eh . , end table	Inverse Relations and Functions (Lesson 6-7) The inverse of y = x + 2 , x ≥ 0 , y ≥ 2 is  x = y + 2 , or  y = x − 2 , or  y = ( x − 2 ) 2 , y ≥ 0 , x ≥ 2. table with 3 rows and 1 column , row1 column 1 , y equals square root of x plus 2 comma x greater than or equal to 0 comma y greater than or equal to 2 , row2 column 1 , is x equals square root of y plus 2 comma or , square root of y equals x minus 2 comma , row3 column 1 , or y equals . open , x minus 2 , close squared . comma y greater than or equal to 0 comma x greater than or equal to 2. , end table	Graphing Radical Functions (Lesson 6-8)

Choose the correct term to complete each sentence.

1. The number under a radical sign is called the (index/radicand).
2. (Radical functions/Inverse functions) are of the form f ( x ) = x n . f , open x close , equals , the th , root of x , , .
3. A radical expression can always be rewritten using a(n) (rational exponent/inverse relation).
4. When two functions are combined so the range of one becomes the domain of the other, the resulting function is called a (square root function/composite function).

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