Radical functions

Definition

A radical function is a function that includes a variable within a radical, such as a square root or cube root. These functions often involve expressions like $\sqrt{x}$ or $\sqrt[3]{x}$ and are the inverse of polynomial functions to some degree.

5 Must Know Facts For Your Next Test

1. The domain of a radical function depends on the index of the radical; for even indices, the radicand must be non-negative.
2. Radical functions can be transformed similarly to other functions (shifts, stretches, compressions).
3. The inverse of a quadratic function is typically a square root function.
4. Simplifying expressions with radicals often involves rationalizing the denominator if necessary.
5. Graphing radical functions usually requires identifying key points and understanding the general shape of the curve.

Review Questions

• What is the domain of the function $f(x) = \sqrt{x-3}$?
• How would you transform the graph of $y = \sqrt{x}$ to obtain the graph of $y = \sqrt{x-2} + 1$?
• What is the inverse function of $f(x) = x^2$ restricted to $x \geq 0$?

Related terms

Polynomial Functions: Functions that involve only non-negative integer powers of x.

Rational Functions: Functions defined by a ratio of two polynomials.

Inverse Functions: $f^{-1}(x)$ represents an inverse if $(f(f^{-1}(x)) = x)$ and $(f^{-1}(f(x)) = x)$ for all x in their domains.