Graphs of radical functions

Front

What is a radical function?

Back

A radical function is a function that contains a variable within a radical, such as a square root or cube root. The general form is f(x) = √(x) or f(x) = ∛(x).

Front

What is the parent function of a square root function?

Back

The parent function of a square root function is f(x) = √(x).

Front

What transformations occur when a function is shifted vertically?

Back

A vertical shift moves the graph up or down. For example, f(x) + k shifts the graph up by k units, while f(x) - k shifts it down by k units.

Front

What does it mean to compress a graph vertically?

Back

A vertical compression occurs when the graph is squeezed towards the x-axis. This is represented by multiplying the function by a factor between 0 and 1, such as f(x) = 1/2 * √(x).

Front

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

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, there is a corresponding point (x, -y). This is represented by f(x) = -√(x).

Front

How do you identify the domain of a radical function?

Back

The domain of a radical function is determined by the values of x for which the expression under the radical is non-negative. For example, for f(x) = √(x - 2), the domain is x ≥ 2.

Front

What is the range of the square root function?

Back

The range of the square root function f(x) = √(x) is [0, ∞), meaning it includes all non-negative real numbers.

Front

What is a cube root function?

Back

A cube root function is a function of the form f(x) = ∛(x), which represents the inverse operation of cubing a number.

Front

What transformations occur when a function is shifted horizontally?

Back

A horizontal shift moves the graph left or right. For example, f(x - h) shifts the graph right by h units, while f(x + h) shifts it left by h units.

Front

What is the effect of a vertical stretch on a graph?

Back

A vertical stretch occurs when the graph is pulled away from the x-axis. This is represented by multiplying the function by a factor greater than 1, such as f(x) = 2 * √(x).