Transformations of Square Root Functions

Front

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

Back

[0, infinity)

Front

What transformation occurs when the function f(x) = √x is changed to f(x) = √(x - 3)?

Back

The graph shifts 3 units to the right.

Front

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

Back

[0, infinity)

Front

How does the graph of f(x) = -√x differ from f(x) = √x?

Back

The graph of f(x) = -√x is a reflection of f(x) = √x across the x-axis.

Front

What happens to the graph of f(x) = √x when a constant is added, such as f(x) = √x + 2?

Back

The graph shifts 2 units up.

Front

What is the effect of multiplying the square root function by a negative number, such as f(x) = -2√x?

Back

The graph is reflected across the x-axis and stretched vertically by a factor of 2.

Front

What is the domain of the function f(x) = √(x + 4)?

Back

[-4, infinity)

Front

If f(x) = √(x - 1) + 3, what is the vertical shift of the graph?

Back

The graph shifts 3 units up.

Front

What transformation occurs when the function f(x) = √(2x)?

Back

The graph is vertically compressed by a factor of 1/√2.

Front

What is the effect of the transformation f(x) = √(x) - 5?

Back

The graph shifts 5 units down.