graphing radical functions

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) = oot[n]{g(x)}@@ where g(x) is a polynomial.

Front

How does the graph of @@y = oot{(x)}@@ look?

Back

The graph of @@y = oot{(x)}@@ is a curve that starts at the origin (0,0) and increases gradually to the right, remaining in the first quadrant.

Front

What effect does the equation @@y = oot{(x - h)}@@ have on the graph?

Back

The equation shifts the graph of the radical function to the right by h units.

Front

What effect does the equation @@y = oot{(x)} + k@@ have on the graph?

Back

The equation shifts the graph of the radical function up by k units.

Front

What is the domain of the function @@y = oot{(x)}@@?

Back

Front

How do you determine the domain of a radical function?

Back

To determine the domain of a radical function, set the expression inside the radical greater than or equal to zero and solve for x.

Front

What is the range of the function @@y = oot{(x)}@@?

Back

Front

What does the equation @@y = oot{(x - 5)} - 1@@ represent?

Back

This equation shifts the graph of the radical function right 5 units and down 1 unit.

Front

What is the effect of the negative sign in front of the radical, e.g., @@y = - oot{(x)}@@?

Back

The negative sign reflects the graph of the radical function across the x-axis.

Front

How do you find the x-intercept of a radical function?

Back

To find the x-intercept, set the function equal to zero and solve for x.