Graphing Square Root and Cube Root Functions

This video tutorial covers how to graph square root and cube root functions. It begins with an introduction to the parent functions and explains how to graph them using specific values. The video then discusses the general form of these functions and how transformations such as stretching, compressing, and shifting affect their graphs. The tutorial also highlights the differences between square root and cube root functions, particularly in terms of domain and range. Finally, the video offers additional resources for students preparing for standardized tests like the ACT and SAT.

What is the parent function for square root functions?

• y = x^2

• y = √x

• y = 1/x

• y = x^3

Which of the following values is NOT suitable for graphing the parent square root function?

• -1

• 1

• 4

• 0

What is the domain of the basic square root function y = √x?

• x ≤ 0

• x ≥ 0

• All real numbers

• x > 0

How does the value of 'a' in the equation y = a√(x - h) + k affect the graph?

• It shifts the graph left or right

• It shifts the graph up or down

• It reflects the graph over the y-axis

• It stretches or compresses the graph vertically

If the equation is y = √(x - 2) + 3, how is the graph shifted?

• Right 2, Down 3

• Left 2, Down 3

• Right 2, Up 3

• Left 2, Up 3

What is the parent function for cube root functions?

• y = √x

• y = x^2

• y = ³√x

• y = x^3

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

• x ≥ 0

• x > 0

• All real numbers

• x ≤ 0

How does the value of 'k' in the equation y = a³√(x - h) + k affect the graph?

• It shifts the graph left or right

• It shifts the graph up or down

• It stretches or compresses the graph vertically

• It reflects the graph over the y-axis

In the equation y = -½³√(x + 3) - 4, what does the negative sign in front of ½ indicate?

• The graph is shifted left

• The graph is shifted down

• The graph is compressed vertically

• The graph is reflected over the x-axis

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

• y > 0

• y ≤ 0

• y ≥ 0

• All real numbers