Characteristics of 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

What is the parent function of a square root function?

Back

The parent function of a square root function is @@f(x) = oot{ x }@@.

Front

What does it mean to shift a graph left or right?

Back

Shifting a graph left or right involves adding or subtracting a value from the input variable (x). For example, @@f(x) = oot{ x - 2 }@@ shifts the graph 2 units to the right.

Front

What does it mean to shift a graph up or down?

Back

Shifting a graph up or down involves adding or subtracting a value from the output variable (y). For example, @@f(x) = oot{ x } + 3@@ shifts the graph 3 units up.

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. For example, @@f(x) = - oot{ x }@@ reflects the parent function.

Front

How do you determine the domain of a radical function?

Back

Front

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

Back

Front

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

Back

Reflecting a graph over the y-axis means that for every point (x, y) on the graph, there is a corresponding point (-x, y). This is achieved by replacing x with -x in the function.

Front

What transformations occur in the function @@f(x) = - oot{ x - 2 } + 1@@?

Back

The function is shifted right 2 units, reflected over the x-axis, and shifted up 1 unit.

Front

What is the domain of the function @@f(x) = -3 oot{3x - 15} + 4@@?

Back