Transformations of Square and Cube Root Functions

Front

What is the parent function of a square root function?

Back

f(x) = √x, defined for x ≥ 0.

Front

What is the parent function of a cube root function?

Back

f(x) = ∛x, defined for all real numbers.

Front

What does it mean to shift a graph to the right?

Back

The graph moves horizontally to the right by a specified number of units.

Front

What does it mean to shift a graph up?

Back

The graph moves vertically upwards by a specified number of units.

Front

What is the effect of reflecting a graph over the x-axis?

Back

The y-values of the function are multiplied by -1.

Front

What is the effect of reflecting a graph over the y-axis?

Back

The x-values of the function are multiplied by -1.

Front

What is the domain of all square root functions?

Back

[0, ∞) - all non-negative real numbers.

Front

What is the range of all cube root functions?

Back

(-∞, ∞) - all real numbers.

Front

How does a vertical stretch affect the graph of a function?

Back

It multiplies the y-values of the function by a factor greater than 1.

Front

What does a downward shift of 2 units look like on a graph?

Back

The entire graph moves down by 2 units.