Transformations of Functions

The video tutorial explains how to apply transformations to the square root function. It covers replacing x with x-3 inside the function and subtracting 2 outside the function. The tutorial also discusses how these transformations affect the domain and range of the function, shifting the domain to x ≥ 3 and the range to y ≥ -2.

What is the main focus of the problem discussed in the video?

• Applying transformations to a linear function

• Applying transformations to a quadratic function

• Applying transformations to the square root function

• Applying transformations to a cubic function

In the transformation inside the function, what is x replaced with?

• x + 3

• x - 3

• x / 3

• x * 3

What is the effect of replacing x with x - 3 inside the function?

• Stretches the graph vertically

• Compresses the graph horizontally

• Shifts the graph 3 units to the right

• Shifts the graph 3 units to the left

What operation is performed outside the function in the transformation?

• Multiplying by 2

• Subtracting 2

• Adding 2

• Dividing by 2

What is the effect of subtracting 2 outside the function?

• Compresses the graph vertically

• Stretches the graph horizontally

• Shifts the graph 2 units down

• Shifts the graph 2 units up

What is the original domain of the square root function?

• x is greater than or equal to -2

• x is greater than or equal to 3

• x is greater than or equal to 0

• x is greater than or equal to -3

After the transformation, what is the new domain of the function?

• x is greater than or equal to 0

• x is greater than or equal to -2

• x is greater than or equal to 3

• x is greater than or equal to -3

What is the original range of the square root function?

• y is greater than or equal to 3

• y is greater than or equal to -2

• y is greater than or equal to 0

• y is greater than or equal to -3

After the transformation, what is the new range of the function?

• y is greater than or equal to -3

• y is greater than or equal to 0

• y is greater than or equal to -2

• y is greater than or equal to 3

What happens to the graph of the square root function when it is shifted 3 units to the right?

• The graph moves 3 units down

• The graph moves 3 units up

• The graph moves 3 units to the left

• The graph moves 3 units to the right