Transformations of the Basic Square Root Function

This video tutorial covers transformations of the basic square root function. It begins with a review of the square root function and its graph, followed by an exploration of reflections across the X and Y axes. The tutorial then explains vertical and horizontal shifts, as well as vertical and horizontal stretches and compressions. Each transformation is demonstrated with animations, and the effects on the function's graph are analyzed. The video concludes with a summary of the transformations and their impacts on the function's graph.

What is the y-coordinate when x is 4 in the basic square root function?

• 4

• 1

• 3

• 2

What transformation occurs when the function is reflected across the x-axis?

• The function shifts down

• The function shifts up

• The x-coordinates change sign

• The y-coordinates change sign

How does the function change when it is reflected across the y-axis?

• The x-coordinates change sign

• The y-coordinates change sign

• The function shifts left

• The function shifts right

What happens to the graph when the function is shifted up by 2 units?

• It moves left

• It moves down

• It moves up

• It moves right

If a function is shifted down by 2 units, what is the transformation?

• Shift down

• Shift up

• Vertical compression

• Vertical stretch

What is the effect of a vertical stretch on the graph of a function?

• The graph shifts down

• The graph becomes wider

• The graph becomes narrower

• The graph shifts up

How does a vertical compression affect the graph of a function?

• The graph shifts left

• The graph becomes narrower

• The graph becomes wider

• The graph shifts right

What transformation occurs when the function undergoes a horizontal compression?

• The graph becomes narrower

• The graph shifts down

• The graph shifts up

• The graph becomes wider

How does a horizontal stretch affect the graph of a function?

• The graph shifts right

• The graph shifts left

• The graph becomes narrower

• The graph becomes wider

What is the reciprocal factor used in a horizontal compression?

• 1/3

• 1

• 1/2

• 2