Transformations of square roots

Front

What is the parent function of square root transformations?

Back

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

Front

What does it mean to reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is a vertical stretch in the context of transformations?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

What is a vertical compression in the context of transformations?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter.

Front

How does shifting a graph to the right affect its equation?

Back

Shifting a graph to the right by 'h' units changes the equation from y = f(x) to y = f(x - h).

Front

How does shifting a graph down affect its equation?

Back

Shifting a graph down by 'k' units changes the equation from y = f(x) to y = f(x) - k.

Front

What is the effect of a negative sign in front of a square root function?

Back

A negative sign in front of a square root function reflects the graph over the x-axis.

Front

What does the transformation y = √(x - 3) represent?

Back

The transformation y = √(x - 3) represents a horizontal shift of the parent function 3 units to the right.

Front

What does the transformation y = √(x) + 3 represent?

Back

The transformation y = √(x) + 3 represents a vertical shift of the parent function 3 units up.

Front

What is the transformation of y = 2√x?

Back

The transformation of y = 2√x is a vertical stretch by a factor of 2.