Algebra II Second Review @FC

Simplify Radicals

100

√10 (√2 +2)

2√5 + 2√10

200

-∛(-135) - ∛(40)

∛5

300

√(28x³y³)

2xy √(7xy)

400

⁷√(512u⁸v³)

2u ⁷√(4uv³)

500

⁴√(48x⁴y⁷) - ⁴√(648x²y⁵)

2xy ⁴√(3y³) -  3y ⁴√(8x²y)

Find the Zeros/Asymptotes/Holes

100

y = 1/x

Vertical asymptote at x=0

Horizontal asymptote at y=0

200

y = (x-3) / (x+21)

Vertical Asymptote: x=-21,

Horizontal Asymptote: y=1

300

y= (3x-5) / (4x²-x-3)

Vertical asymptote: x=-3/4 & x=1

Horizontal asymptote: y=0

400

y= (5x²+14x+8) /       (x²-9x-22)

Vertical asymptote: x=11

Horizontal asymptote: y=5

Hole : x=-2    (-2, 6/13)

500

y = (3x-3)(x-4)    /

      (x-4)(x+7)(2x+5)

Vertical asymptote: x=-7  &  x=5/2

Horizontal asymptote: y=0

Hole: x=4    (4, 3/11)

Solve Radicals

100

√(110 - n) = n

10

200

√(5x-4) - 9 = 0

x = 17

300

⁴√(3x−2) + 3 = 5 

x = 6

400

√(2x-5) + √(2x) = 5

x = 9/2

500

√(2x-12) - x = 6

x = -6, -4

Adding/Subtracting rational expressions

100

6/(x-1)    -     (5x)/4

(24 − 5x² + 5x)    /       4(x − 1)

200

((x/25)  -   (x/5))     /   x

-4/25

300

(5x+5)/(5x²+35x-40)    +   (7x)/(3x)

(7x²+52x-53) / 3(x+8)(x-1)

400

x  -   (1/y)  -   (x² /(x-y))

(-xy²-x+y)  /  (y(x-y))

500

5x/(1-2x)   -   2x/(2x+1)   +  3/(4x²-1)

(-14x²-3x+3)   /  (2x+1)(2x-1)

End Behavior/ Domain/Range

100

y = x³+75

x→ +∞   y→+∞;

x→ -∞    y→-∞

domain (-∞,+∞)

range (-∞, +∞)

200

y = x²+x+1

x→ +∞   y→+∞;

x→ -∞    y→+∞

domain (-∞,+∞)

range [3/4, +∞)

300

y = x / (x²-6x+8)  

Don't find the range

x→ +∞   y→0;

x→ -∞    y→0

domain (-∞,2)∪(2,4)∪(4,+∞)

range  (-∞, -√2-1.5)∪(√2-1.5, +∞)

400

y = √(x-5)  + 2

x→ +∞   y→+∞;

domain [5,+∞)

range  [2,+∞)

500

 y = x^-3 + 3x

dont find range

x→ +∞   y→+∞;

x→ -∞    y→-∞

domain (-∞,0)(0,+∞)

range (-∞,-4) (4, +∞)