Radical Functions and Equations

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, cube root, etc. The general form is @@f(x) = oot[n]{g(x)}@@ where g(x) is a polynomial.

Front

What does the expression @@y = rac{1}{a} imes oot[n]{x} + b@@ represent?

Back

This expression represents a radical function that has been transformed. The parameter 'a' affects the vertical stretch or compression, and 'b' represents a vertical translation.

Front

What is a vertical stretch in the context of radical functions?

Back

A vertical stretch occurs when the value of 'a' in the function @@y = a oot[n]{x}@@ is greater than 1, making the graph of the function steeper.

Front

What does a vertical translation of 'k' units mean?

Back

A vertical translation of 'k' units means the graph of the function moves up if 'k' is positive and down if 'k' is negative.

Front

Back

The graph shifts horizontally to the right by 'h' units and vertically by 'k' units.

Front

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

Back

A negative sign reflects the graph of the function over the x-axis.

Front

What transformation does the equation @@y = oot[n]{x} - 3@@ represent?

Back

This equation represents a vertical translation down by 3 units.

Front

What does the term 'horizontal translation' refer to?

Back

Horizontal translation refers to shifting the graph left or right along the x-axis, determined by the value of 'h' in the equation @@y = oot[n]{x - h}@@.

Front

What is the significance of the index 'n' in a radical function?

Back

The index 'n' indicates the degree of the root. For example, if n=2, it is a square root; if n=3, it is a cube root.

Front

How do you identify a vertical stretch from the equation @@y = 3 oot{2}{x}@@?

Back

The coefficient '3' indicates a vertical stretch by a factor of 3.