Understanding Square Root Functions and Transformations

This video tutorial covers graphing the square root function and explores vertical and horizontal stretches and compressions. It begins with the basic square root function, explaining its domain and graphing it using a table of values. The tutorial then compares this to functions with vertical stretches and compressions, illustrating how these transformations affect the graph. It also covers horizontal compressions and stretches, explaining the changes in the graph's appearance and the mathematical reasoning behind these transformations.

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 NOT on the graph of the basic square root function?

• (2, 3)

• (4, 2)

• (1, 1)

• (0, 0)

How does the graph of g(x) = 2√x differ from the basic square root function?

• It is shifted to the right.

• It is compressed vertically by a factor of 2.

• It is stretched vertically by a factor of 2.

• It is reflected over the x-axis.

What is the effect of multiplying the square root function by a constant greater than 1?

• Horizontal stretch

• Vertical stretch

• Vertical compression

• Horizontal compression

In the function h(x) = 1/2√x, what transformation occurs compared to the basic square root function?

• Horizontal stretch by a factor of 2

• Vertical compression by a factor of 1/2

• Vertical stretch by a factor of 2

• Horizontal compression by a factor of 1/2

What is the domain of the function g(x) = √(2x)?

• x ≤ 0

• x > 0

• x ≥ 0

• x < 0

How does the graph of g(x) = √(2x) compare to the basic square root function?

• It is a horizontal compression.

• It is a horizontal stretch.

• It is a vertical stretch.

• It is a vertical compression.

In the function h(x) = √(1/2x), what transformation occurs compared to the basic square root function?

• Vertical stretch by a factor of 2

• Horizontal compression by a factor of 2

• Vertical compression by a factor of 2

• Horizontal stretch by a factor of 2

What happens to the x-coordinates in a horizontal stretch transformation?

• They are added to the factor.

• They remain unchanged.

• They are divided by the factor.

• They are multiplied by the factor.

If a function is horizontally compressed by a factor of 1/2, what happens to the x-coordinates?

• They are halved.

• They are doubled.

• They are tripled.

• They remain the same.