Graphs of radical functions

Front

What is a cube root function?

Back

A cube root function is a function of the form f(x) = @@ oot{3}{x}@@, which represents the inverse operation of cubing a number.

Front

What is the parent function of a square root function?

Back

The parent function of a square root function is f(x) = @@ oot{2}{x}@@.

Front

What does it mean for a graph to be reflected over the x-axis?

Back

A reflection over the x-axis means that for every point (x, y) on the graph, there is a corresponding point (x, -y).

Front

What is a vertical stretch in graph 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

How do you identify the transformations of a function compared to its parent function?

Back

Transformations can be identified by looking for shifts (horizontal or vertical), reflections, and stretches/compressions in the function's equation.

Front

What is the domain of the function f(x) = @@ oot{3}{x}@@?

Back

The domain of the cube root function f(x) = @@ oot{3}{x}@@ is all real numbers, or (-∞, ∞).

Front

What is the range of the function f(x) = @@ oot{2}{x}@@?

Back

The range of the square root function f(x) = @@ oot{2}{x}@@ is [0, ∞).

Front

What does it mean for a function to be vertically compressed?

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

What is the effect of shifting a graph 5 units to the right?

Back

Shifting a graph 5 units to the right means replacing x with (x - 5) in the function's equation.

Front

What is the transformation of the function f(x) = - oot{2}{x} + 3?

Back

The function is reflected over the x-axis and shifted up 3 units.