5.7 – Graphing Radical Functions

Objective: Students will be able to graph and transform radical functions.

Radical Functions Radical function – a function whose rule is a radical

expression.Square root function – a radical function involving a

square root. Square root parent function: f(x) = √x

The Parent Radical FunctionExample 1: Graph the function, and identify its domain

and range.f(x) = √xDomain:Range:

x f(x) = √x (x, f(x))

01

4

9

Example 2f(x) =Domain:Range:

x f(x) = (x, f(x))

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Transformations of Square Root FunctionsVertical translation: f(x) = √x + k

+k = up; - k = downHorizontal translation: f(x) = √(x – h)

(x – h) = right; (x + h) = leftReflection:

Across x- axis: f(x) = - √x Across y- axis: f(x) = √-x

Directions: Using the graph of f(x) = √x as a guide, describe the transformation and graph each function.

Example 3: f(x) = √x + 3Transformation:

Example 4: f(x) = √(x – 2)Transformation:

Example 5: f(x) = -√x – 1 Transformation(s):

Your turn…Example 6: f(x) = √-x – 4

Homework for tonightHomework # ____

Textbook pg. 372 # 24, 30, 31, 35