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 shifted 3 units to the right?

Back

f(x) = √(x - 3)

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

It is reflected over the x-axis.

Front

What is the effect of multiplying the square root function by a factor of 2, f(x) = 2√x?

Back

It vertically stretches the graph by a factor of 2.

Front

What is the effect of subtracting 4 from the square root function, f(x) = √x - 4?

Back

It shifts the graph down 4 units.

Front

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

Back

[-2, infinity)

Front

What transformation occurs when the function f(x) = √x is reflected over the y-axis?

Back

This transformation is not applicable to the square root function as it is not defined for negative x.

Front

What is the effect of adding 5 to the square root function, f(x) = √x + 5?

Back

It shifts the graph up 5 units.

Front

What is the general form of a transformed square root function?

Back

f(x) = a√(x - h) + k, where (h, k) is the vertex.