Graph Transformations of Root Functions

The video tutorial covers graphing transformations of square and cube roots, focusing on vertical and horizontal shifts, stretching, and flipping. It explains how these transformations affect the domain and range of the graphs. The tutorial provides step-by-step instructions on applying these transformations, using examples to illustrate the changes in graph shapes and positions. The video concludes with a summary of the key concepts and transformations discussed.

What is the effect of adding a constant outside the square root on the graph?

• Shifts the graph to the left

• Shifts the graph upwards

• Reflects the graph over the x-axis

• Stretches the graph vertically

How does the domain of a square root graph change when it is shifted upwards?

• The domain becomes all real numbers

• The domain remains the same

• The domain shifts to the right

• The domain shifts to the left

What happens to the range of a square root graph when it is shifted upwards?

• The range remains unchanged

• The range starts from a higher value

• The range becomes all real numbers

• The range starts from a lower value

What is the effect of a negative coefficient on a square root graph?

• It shifts the graph downwards

• It stretches the graph horizontally

• It reflects the graph over the x-axis

• It shifts the graph to the right

How does a negative coefficient affect the stretching of a square root graph?

• It compresses the graph vertically

• It stretches the graph vertically

• It stretches the graph horizontally

• It compresses the graph horizontally

What is the effect of adding a constant inside the cube root on the graph?

• Reflects the graph over the y-axis

• Shifts the graph to the right

• Shifts the graph upwards

• Shifts the graph to the left

How does the domain of a cube root graph change with horizontal shifts?

• The domain shifts to the right

• The domain shifts to the left

• The domain remains the same

• The domain becomes all real numbers

What is the effect of a vertical stretch on a cube root graph?

• It compresses the graph vertically

• It compresses the graph horizontally

• It stretches the graph vertically

• It stretches the graph horizontally