Rational Exponents and Radical Functions

nth Roots, Radicals, and Radical Exponents

99

 root(3)(8y^9) 

2y^3

100

 root(4)(x^2) 

 sqrt(x) 

100

 root(8)(v^8g^40) 

pmvg^5

100

 root(6)(729a^24b^18 

pm3a^4b^3

Properties of Exponents and Radicals

99

  root(3)(4) (6 root(3)(3) -1)

6 root(3)(12)-  root(3)(4) 

100

 root(4)(2) x  root(4)(32) 

2 root(4)(2) 

100

 frac{6}{1+sqrt2 

-6+6sqrt2

100

 (5sqrt3+6)(5sqrt3-6) 

39

Graphing Radical Functions

99

What transformation does the following equation have?

 f(x)=root(3)(x-3) 

right 3 units

100

What transformation does the following equation have? f(x)=sqrtx+1 

up one unit

100

Rewrite the radical function and what transformation does the following equation have?  f(x)=sqrt(4x-24)-6 

stretch by a factor of 2

right 6 units

down 3 units

100

Rewrite the radical function and what transformation does the following equation have?  f(x)=sqrt(25x+75) 

Vertical stretch by 5

3 units right

Solving Radical Equations

99

 13-root(4)(x)=10 

81

100

 sqrt(6x-20)-x=6 

4, 14

4 is extraneous

100

 sqrt(5x+1)+1=x 

0, 7

0 is extraneous

Function Operations

99

Let f(x)=-x+6  and  g(x)=5x. What is g(f(2)).

20

100

 Let f(x)=-x+6  and  g(x)=5x .

What is f+g?

4x+6

100

Let  f(x)=x^2+x and g(x)=9-2x. What is  fcircg ?

4x^2-38x+90

100

Let  f(x)=3x^2-2x+6 and g(x)=7x-4. What is f+g

3x^2+5x+2

nth Roots, Radicals, and Radical Exponents

99

Simplify  root(4)(16) 

2, -2

100

What is   81^(1/4) 

3,-3

100

 root(3)(27x^12) 

 3x^(4) 

100

 6y^(3)=750 

5

100

 f(x)=x^2+5 and g(x)=sqrt(x)-5 Are the two functions inverses of each other?

Nope