Transformations of Square Root Functions

Front

What is the parent function of a square root function?

Back

The parent function of a square root function is y = √x.

Front

What transformation occurs when the function is written as y = √(x - 2)?

Back

The function is shifted right 2 units.

Front

What transformation occurs when the function is written as y = √(x) + 3?

Back

The function is shifted up 3 units.

Front

What is the effect of a negative sign in front of the square root function, such as y = -√x?

Back

The function is reflected over the x-axis.

Front

How does the equation y = √(x + 4) - 1 transform the parent function?

Back

The function is shifted left 4 units and down 1 unit.

Front

What is the domain of the function y = √(x - 1)?

Back

The domain is [1, ∞).

Front

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

Back

The range is [2, ∞).

Front

If a square root function is shifted down 2 units, how is it represented mathematically?

Back

It is represented as y = √x - 2.

Front

What transformation does the equation y = √(x - 5) - 1 represent?

Back

It shifts the function right 5 units and down 1 unit.

Front

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

Back

The range is (-∞, 3].