Exploring Radical Functions and Exponents

Simplify the expression: (x^{\frac{3}{2}})^2.

• x^3

• x^{\frac{3}{4}}

• x^{\frac{5}{2}}

• x^{\frac{3}{2}}

What is the simplified form of \sqrt[3]{x^5}?

• x^{\frac{5}{3}}

• x^{\frac{3}{5}}

• x^{\frac{1}{3}}

• x^{\frac{5}{6}}

Which of the following is the graph of y = \sqrt{x}?

• A line passing through the origin

• A parabola opening upwards

• A curve starting at the origin and increasing to the right

• A horizontal line

Identify the domain of the function f(x) = \sqrt{x - 4}.

• x \geq 4

• x > 4

• x \leq 4

• All real numbers

What is the range of the function f(x) = \sqrt{x} + 2?

• y \geq 2

• y > 2

• y \leq 2

• All real numbers

Solve the equation \sqrt{x + 3} = 5.

• x = 22

• x = 28

• x = 25

• x = 20

Which of the following is the transformation of the function y = \sqrt{x} to y = \sqrt{x - 2} + 3?

• Shift right 2 units, up 3 units

• Shift left 2 units, up 3 units

• Shift right 2 units, down 3 units

• Shift left 2 units, down 3 units

Simplify the expression: (x^{\frac{1}{4}} \cdot x^{\frac{1}{2}}).

• x^{\frac{3}{4}}

• x^{\frac{1}{8}}

• x^{\frac{3}{2}}

• x^{\frac{5}{4}}

What is the solution to the equation x^{\frac{3}{2}} = 8?

• x = 4

• x = 16

• x = 8

• x = 64

If f(x) = \sqrt{x}, what is f(9)?

• 3

• 9

• 81

• 27