2.1 Radical Functions & Transformations

Front

What is a radical function?

Back

A radical function is a function that contains a variable within a radical (square root, cube root, etc.). The general form is f(x) = √(g(x)), where g(x) is a polynomial.

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 does a vertical stretch do to the graph of a function?

Back

A vertical stretch multiplies the output values of the function by a factor greater than 1, making the graph taller.

Front

What is a horizontal translation?

Back

A horizontal translation shifts the graph of a function left or right along the x-axis.

Front

What does a reflection over the x-axis do to a function's graph?

Back

A reflection over the x-axis flips the graph of the function upside down.

Front

How do you represent a vertical translation of a function?

Back

A vertical translation is represented by adding or subtracting a constant from the function, f(x) + k, where k is the vertical shift.

Front

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

Back

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

Front

What transformations occur when the function is written as f(x) = √(x - 2) + 3?

Back

This function represents a horizontal translation 2 units to the right and a vertical translation 3 units up.

Front

What is the effect of a positive constant added to a radical function?

Back

Adding a positive constant to a radical function translates the graph upward.

Front

What does the notation f(x) = -√(x + 5) indicate about the graph?

Back

This notation indicates that the graph is reflected over the x-axis and translated 5 units to the left.