Understanding Domain and Range of Square Root Functions

The video tutorial explains how to find the domain and range of square root functions. It begins with a review of the concepts of domain and range, emphasizing that the radicand in square root functions cannot be negative. The tutorial then explores the domain and range of three specific functions: the basic square root function, G(x) = √(x + 3), and H(x) = √(3 - 2x) - 4. For each function, the video demonstrates how to express the domain and range using inequalities and interval notation, and verifies these graphically.

What is the domain of a function?

• The set of all possible outputs

• The set of all possible inputs

• The set of all positive numbers

• The set of all negative numbers

Why can't the radicand in a square root function be negative?

• It would result in a negative number

• It would result in a zero

• It would result in a complex number

• It would result in a positive number

What is the range of the basic square root function?

• Y is less than or equal to zero

• Y is greater than or equal to zero

• Y is less than zero

• Y is equal to zero

How is the function g(x) = √(x + 3) related to the basic square root function?

• It is shifted right by three units

• It is shifted left by three units

• It is shifted up by three units

• It is shifted down by three units

What is the domain of g(x) = √(x + 3)?

• X is less than or equal to 3

• X is greater than or equal to 3

• X is less than or equal to -3

• X is greater than or equal to -3

What is the range of g(x) = √(x + 3)?

• Y is less than zero

• Y is greater than or equal to zero

• Y is equal to zero

• Y is less than or equal to zero

What is the domain of h(x) = √(3 - 2x) - 4?

• X is greater than or equal to -3/2

• X is less than or equal to -3/2

• X is greater than or equal to 3/2

• X is less than or equal to 3/2

What is the range of h(x) = √(3 - 2x) - 4?

• Y is greater than or equal to 4

• Y is less than or equal to 4

• Y is less than or equal to -4

• Y is greater than or equal to -4

What happens to the inequality when dividing by a negative number?

• The inequality becomes an equality

• The inequality reverses

• The inequality is eliminated

• The inequality remains the same

What is the smallest value of the function h(x) = √(3 - 2x) - 4?

• 0

• -3

• -4

• 4