Transformations of Cube and Square Root Functions

The video tutorial covers graphing transformations of square and cube roots. It explains how to shift graphs vertically and horizontally, stretch them, and reflect them. The tutorial provides examples of transformations, including vertical shifts, horizontal shifts, and vertical stretches, and discusses the impact on domain and range. The video concludes with a summary of key concepts and transformations.

What happens to a graph when a constant is added outside the square root function?

• The graph reflects over the x-axis.

• The graph stretches horizontally.

• The graph shifts vertically.

• The graph shifts horizontally.

If a square root graph is shifted up by 3 units, what happens to its range?

• The range remains the same.

• The range becomes all real numbers.

• The range starts at -3.

• The range starts at 3.

How does a negative sign inside the cube root function affect the graph?

• It shifts the graph to the left.

• It shifts the graph to the right.

• It reflects the graph over the x-axis.

• It reflects the graph over the y-axis.

What is the effect of multiplying the output of a cube root function by 2?

• The graph shifts up by 2 units.

• The graph stretches vertically.

• The graph compresses vertically.

• The graph shifts down by 2 units.

In a square root transformation, what does a negative sign outside the function indicate?

• The graph shifts to the right.

• The graph reflects over the y-axis.

• The graph shifts to the left.

• The graph reflects over the x-axis.

What is the result of shifting a cube root graph to the right by 2 units?

• The graph moves right by 2 units.

• The graph moves left by 2 units.

• The graph moves up by 2 units.

• The graph moves down by 2 units.

How does adding a constant inside the square root function affect the graph?

• It shifts the graph up.

• It shifts the graph down.

• It shifts the graph left.

• It shifts the graph right.

What happens to the domain of a cube root function when it is transformed?

• The domain becomes all negative numbers.

• The domain becomes non-negative numbers.

• The domain remains all real numbers.

• The domain becomes all positive numbers.

If a square root graph is reflected over the x-axis, what happens to its range?

• The range becomes all real numbers.

• The range remains the same.

• The range becomes all positive numbers.

• The range becomes all negative numbers.

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

• The graph becomes wider.

• The graph becomes narrower.

• The graph shifts down.

• The graph shifts up.