Determine the domain of a radical multiplied by a variable

The video tutorial explains how to determine the domain of a function involving a quadratic term and a radical. It begins by introducing the function and identifying the quadratic component. The focus then shifts to the radical, emphasizing the importance of the radicand being non-negative to define the domain. The instructor demonstrates solving the inequality to find the domain and discusses graphing the solution. The domain is expressed in interval notation, and the tutorial concludes with a summary of the key points.

What type of function is y = X^2 * sqrt(2X - 3)?

• Logarithmic

• Exponential

• Quadratic

• Linear

Why is it important to focus on the radicand when determining the domain of the function?

• Because it affects the symmetry of the function

• Because it affects the range of the function

• Because it determines the continuity of the function

• Because it must be positive for the function to be defined

What inequality must be solved to find the domain of the function y = X^2 * sqrt(2X - 3)?

• 2X - 3 >= 0

• 2X - 3 <= 0

• 2X - 3 > 0

• 2X - 3 < 0

What is the solution to the inequality 2X - 3 >= 0?

• X <= 3/2

• X >= 3/2

• X > 3/2

• X < 3/2

How is the domain of the function y = X^2 * sqrt(2X - 3) expressed in interval notation?

• [3/2, Infinity]

• [3/2, Infinity)

• (3/2, Infinity]

• (3/2, Infinity)