Transformations of Square and Cube Root Functions

Front

What is a square root function?

Back

A square root function is a function of the form f(x) = √x, where the output is the non-negative square root of x. The graph of this function starts at the origin (0,0) and increases gradually.

Front

What is a cube root function?

Back

A cube root function is a function of the form f(x) = ∛x, where the output is the cube root of x. The graph passes through the origin and extends into all four quadrants.

Front

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

Back

Shifting a function to the right means adding a positive value to the x-variable in the function's equation. For example, f(x) = √(x - 2) shifts the graph of f(x) = √x two units to the right.

Front

What does it mean to shift a function up?

Back

Shifting a function up means adding a positive value to the entire function. For example, f(x) = √x + 3 shifts the graph of f(x) = √x three units up.

Front

What is a vertical stretch of a function?

Back

A vertical stretch occurs when the output of the function is multiplied by a factor greater than 1. For example, f(x) = 2√x stretches the graph of f(x) = √x vertically by a factor of 2.

Front

What is a reflection over the x-axis?

Back

A reflection over the x-axis occurs when the output of the function is multiplied by -1. For example, f(x) = -√x reflects the graph of f(x) = √x over the x-axis.

Front

What is the parent function of square root functions?

Back

The parent function of square root functions is f(x) = √x, which has a domain of [0, ∞) and a range of [0, ∞).

Front

What is the parent function of cube root functions?

Back

The parent function of cube root functions is f(x) = ∛x, which has a domain and range of all real numbers (ℝ).

Front

How do you describe a translation of a function?

Back

A translation of a function involves shifting the graph horizontally or vertically without changing its shape. This can be described using the terms 'left', 'right', 'up', or 'down'.

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. For example, f(x) = -√x reflects the graph of f(x) = √x.