Radical and Rational Exponents Review

What is the Range of ALL Cube Root Functions?

• (−∞,∞)

• [0,∞)

• (−∞,0]

• All Cube Root Functions are different.

Which function matches the graph?

• f(x) = √(x - 4) - 2

• f(x) = √(x + 2) - 4

• f(x) = √(x - 2) - 4

• f(x) = √(x + 4) - 2

Find the domain and range of the function
Hint:  Use a scratch graph to help you visualize things. 

• Domain: (-∞, ∞)  Range: [-∞, 4]

• Domain: [1, ∞)  Range: (-∞, 4]

• Domain: [-1. ∞) Range: [4, ∞) 

• Domain: [4, ∞) Range: [-1,∞) 

Solve the radical equation. Do not list extraneous solution as answer. Remember just put # as answer not x = #

Answer explanation

After you cube both sides should get: 4x+23=27 then solve 2 step equation (don't forget to check solution)

Solve the radical equation. Do not list extraneous solution as answer. Remember just put # as answer not x = #

Answer explanation

Need to -6 then divide by 2 before you you do anything else.

$\left(x+20\right)^{\frac{3}{2}}=64$ then multiply to the power of $\frac{2}{3}$ on both sides. Solve the 1 step equation.

Solve the radical equation. Don't forget to check your answers!

• x = -2

• x = 3

• x = 5

• No Solution

• 2^3/5
• -2^3/5
• 2^5/3
• 8⁵

Simplify. Write your final answer using only exponents.