Graphing Square Root and Cube Root Functions

This video tutorial covers graphing square root and cube root functions, focusing on transformations such as vertical stretches, reflections, and translations. It explains the domain and range of these functions and provides example problems to illustrate the concepts. The lesson concludes with a summary of key points and encourages understanding through visual and transformation-based approaches.

What is the domain of the parent function f(x) = √x?

• All negative numbers

• All non-negative numbers

• All positive numbers

• All real numbers

What is the range of the parent function f(x) = √x?

• All real numbers

• All positive numbers

• All negative numbers

• All non-negative numbers

What happens to the graph of y = √x when it is transformed to y = -2√x?

• It is horizontally compressed and reflected over the y-axis

• It is vertically compressed and reflected over the x-axis

• It is shifted up and reflected over the y-axis

• It is vertically stretched by a factor of 2 and reflected over the x-axis

What is the domain of the function y = ³√x?

• All real numbers

• All positive numbers

• All non-negative numbers

• All negative numbers

What is the range of the function y = ³√x?

• All real numbers

• All positive numbers

• All negative numbers

• All non-negative numbers

How is the graph of y = ³√x transformed when it becomes y = ½³√x?

• It is vertically compressed by a factor of 2

• It is horizontally stretched by a factor of 2

• It is vertically stretched by a factor of 2

• It is horizontally compressed by a factor of 2

What is the first step in graphing the function y = 3√(x + 2) - 4?

• Apply the vertical shift

• Apply the horizontal shift

• Apply the vertical stretch

• Reflect over the x-axis

What is the domain of the function y = 3√(x + 2) - 4?

• x ≥ 0

• x ≥ -2

• x ≤ 0

• x ≤ -2

What is the range of the function y = 3√(x + 2) - 4?

• y ≤ 0

• y ≥ -4

• y ≥ 0

• y ≤ -4

What is the final step in graphing the function y = -2³√(x - 2) + 3?

• Apply the vertical stretch

• Apply the horizontal shift

• Reflect over the x-axis

• Apply the vertical shift