Solving and Graphing Radical Functions

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 is the domain of a square root function?

Back

Front

How do you solve a radical equation?

Back

To solve a radical equation, isolate the radical on one side of the equation, then square both sides to eliminate the radical. Check for extraneous solutions afterward.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

Front

What is the range of the square root function?

Back

Front

Describe the transformation: f(x) = -@@ oot{2}{x}@@

Back

The transformation reflects the graph of the square root function over the x-axis.

Front

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

Back

Adding a constant outside the radical, such as in f(x) = @@ oot{2}{x} + k@@, shifts the graph vertically by k units.

Front

What is the effect of multiplying the radical by a negative number?

Back

Multiplying the radical by a negative number reflects the graph over the x-axis.

Front

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

Back

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

Front

What is the vertical asymptote of a radical function?

Back

Radical functions do not have vertical asymptotes, but they may have restrictions on the domain that affect their graph.