Transformations of Radical Functions

Front

What is a radical function?

Back

A radical function is a function that contains a variable within a radical (root) symbol, such as 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 does the A-value in a radical function represent?

Back

The A-value in a radical function affects the vertical stretch or compression and the direction of the graph (upward or downward).

Front

What does the K-value in a radical function represent?

Back

The K-value in a radical function represents a vertical shift of the graph; it moves the graph up if K is positive and down if K is negative.

Front

What does the H-value in a radical function represent?

Back

The H-value in a radical function represents a horizontal shift of the graph; it moves the graph to the right if H is positive and to the left if H is negative.

Front

How does a negative A-value affect the graph of a radical function?

Back

A negative A-value reflects the graph over the x-axis.

Front

What is the effect of adding a constant to the inside of a radical function?

Back

Adding a constant inside the radical function shifts the graph horizontally.

Front

What is the effect of adding a constant outside of a radical function?

Back

Adding a constant outside the radical function shifts the graph vertically.

Front

What is the transformation of the function f(x) = √(x - 4) + 3 compared to the parent function?

Back

The graph is shifted right 4 units and up 3 units.

Front

What is the transformation of the function f(x) = -√(x + 2) - 1 compared to the parent function?

Back

The graph is shifted left 2 units, reflected over the x-axis, and shifted down 1 unit.