Understanding Square Root Functions and Their Reflections

This video tutorial covers graphing the square root function and its reflections across the X and Y axes. It begins with the basic square root function, explaining its domain and graphing process. The tutorial then explores reflections across the X-axis using a negative square root function and across the Y-axis with a negative X inside the square root. Each section includes a table of values and graphical representation to illustrate the changes. The video concludes with a summary of the reflections and their effects on the graph.

What is the domain of the basic square root function f(x) = √x?

• x > 0

• x ≥ 0

• x < 0

• x ≤ 0

Which of the following points is on the graph of the basic square root function?

• (5, 2)

• (3, 3)

• (4, 2)

• (2, 2)

How does the graph of g(x) = -√x differ from the basic square root function?

• It is reflected across the x-axis.

• It is reflected across the y-axis.

• It is shifted down.

• It is shifted up.

What is the y-coordinate of the point on the graph of g(x) = -√x when x = 4?

• 4

• 2

• -2

• -4

For the function h(x) = √(-x), what is the domain?

• x ≤ 0

• x < 0

• x ≥ 0

• x > 0

Which point is on the graph of h(x) = √(-x)?

• (1, 1)

• (-1, 1)

• (1, -1)

• (-1, -1)

What happens to the x-coordinates in the graph of h(x) = √(-x)?

• They change sign.

• They are doubled.

• They remain the same.

• They are halved.

What type of reflection occurs when y = -f(x)?

• No reflection

• Reflection across the x-axis

• Reflection across the origin

• Reflection across the y-axis

In the function h(x) = f(-x), what transformation occurs?

• Reflection across the x-axis

• Horizontal shift

• Reflection across the y-axis

• Vertical shift

Which function represents a reflection across the y-axis?

• f(x) = √x

• h(x) = √(-x)

• g(x) = -√x

• k(x) = x²